Number Theory Integer Types by Michael Carter

Carl Friedrich Gauss was known as one of the top ten greatest mathematicians. He was known as the prince of mathematics. Gauss is quoted calling mathematics the "queen of the sciences" and calling number theory the "queen of mathematics.\342\200\235 Number theory is called "higher arithmetic." Number Theory is the study of whole numbers and sometimes spills over to rational numbers. The whole numbers that is the most fascinating are the primes. We know very little about the primes. Because we know so little about the primes we can make encryption for banks and computer security systems. We also have another fascinating number that we know more about, the composite numbers. The composite numbers are composed of two or more prime\342\200\231s products. There are approximately 10 fields within Number Theory: Elementary, Analytic, Algebraic, Geometry, Combinatorial, Computational, Arithmetic Algebraic, Arithmetic Topology, Arithmetic Dynamics, and Modular Form. All these fields can take advantage of this maple package. This Maple package is called inttypes, which is short for Integer Types. The inttypes package provides over 160 whole number types for Number Theorists to explore numbers. This package may be used as a tool for an academic course, Maple programming, or for research. It is also fun to play with these types for exploration and developing intuition about numbers. In addition, to these number theory integer types, this package also offers three very important functions: ithcomposite, ithprimorial, and printtypes. Maple have a function called, ithprime; which is used to find a particular prime based on its order. This inttypes package provides a function that gives a particular composite number based on its order, called ithcomposite. There is also an ithprimorial function that provides a particular primordial number based on its order. Finally, we have a function that will search among all the types of this package for a particular number and print its type. Srinivasa Ramanujan\342\200\231s taxicab number, 1729, is a good test for printtypes (see below). The number, 3, is also a good test for the printtypes function. On the Number Theory Types Test: Just change the integer on each of the for-loops for larger tests when testing the number theory types. All types return a Boolean value of either true or false. It does not return a number. Note in the testing of the types below we can give input but the output is true or false. The input integer is not the output, hence, do not get confused and begin believing that the input is the output. Finally, there is an official website for referencing and testing the integer types: \342\200\234The On-Line Encyclopedia of Integer Sequences\342\204\242 (OEIS\342\204\242)\342\200\235 located at: http://oeis.org/ I hope you enjoy this package as much as I enjoyed creating it for you. Cheers. ============================================================================================= Application Setup Instructions

=============================================================

This package was designed on Maple 15. It may work on earlier versions of Maple, however, you would need to make modifications in the maple.ini file to make this

happen.

If you have not done so already, extract all the files from the file inttypes.zip to the "C:\134inttypes" folder. These instructions assume that this location is "C:\134inttypes"

Place the maple.ini file in the "C:\134Program Files\134Maple 15\134Users folder" Maple will automatically find this package when you load it using the "with" statement.

If you do not have permission to place files in the "C:\134Program Files\134Maple 15\134Users" folder then see "Alternate Setup Instructions."

Start Maple.

type with(inttypes);

Alternate Setup Instructions

========================================

If you do not have permission to place files in the "C:\134Program Files\134Maple 15\134Users" folder then To do this inside a worksheet, at the prompt, enter the commands:

intlibname := "C:/inttypes":

libname := intlibname, libname:

with(inttypes);

======================================================================================================================

# Number Theory Type Type's Name == =================== ====================== #1) compositenum "Composite Number"

#2) prime "Prime Number" (internal to maple)

#3) semiprime "Semiprime"

#4) almostprime3 "3-Almost Prime"

#5) almostprime4 "4-Almost Prime"

#6) almostprime5 "5-Almost Prime"

#7) almostprime6 "6-Almost Prime"

#8) almostprime7 "7-Almost Prime"

#9) almostprime8 "8-Almost Prime"

#10) almostprime9 "9-Almost Prime"

#11) almostprime10 "10-Almost Prime"

#12) almostprime11 "11-Almost Prime"

#13) almostprime12 "12-Almost Prime"

#14) almostprime13 "13-Almost Prime"

#15) almostprime14 "14-Almost Prime"

#16) almostprime15 "15-Almost Prime"

#17) almostprime16 "16-Almost Prime"

#18) almostprime17 "17-Almost Prime"

#19) almostprime18 "18-Almost Prime"

#20) almostprime19 "19-Almost Prime"

#21) almostprime20 "20-Almost Prime"

#22) perfectnum "Perfect Number"

#23) mersennenum "Mersenne Number"

#24) mersenneexpprime "Mersenne Exponent Prime"

#25) mersenneprime "Mersenne Prime"

#26) doublemersenneprime "Double Mersenne Prime"

#27) fibonaccinum "Fibonacci Number"

#28) fibonacciprime "Fibonacci Prime"

#29) permutableprime "Permutable Prime"

#30) lessertwinprime "Lesser Twin Prime"

#31) greatertwinprime "Greater Twin Prime"

#32) isolatedprime "Isolated Prime"

#33) lessercousinprime "Lesser Cousin Prime"

#34) greatercousinprime "Greater Cousin Prime"

#35) lessersexyprime "Lesser Sexy Prime"

#36) greatersexyprime "Greater Sexy Prime"

#37) eisensteinprime "Eisenstein Prime"

#38) gaussianprime "Gaussian Prime"

#39) repdigitnum "Rep Digit Number"

#40) repunitprime "Rep Unit Prime"

#41) woodallnum "Woodall Number"

#42) woodallprime "Woodall Prime"

#43) palindromicnum "Palindromic Number"

#44) beautifulnum "Beautiful Number"

#45) squarenum "Square Number"

#46) triangularnum "Triangular Number"

#47) oblongnum "Oblong Number"

#48) hexagonalnum "Hexagonal Number"

#49) tetrahedralnum "Tetrahedral Number"

#50) decagonalnum "Decagonal Number"

#51) abundantnum "Abundant Number"

#52) aspiringnum "Aspiring Number"

#53) sociablenum "Sociable Number"

#54) squarefreenum "Square-free Number"

#55) luckynum "Lucky Number"

#56) luckyprime "Lucky Prime"

#57) pentagonalnum "Pentagonal Number"

#58) amicablenum "Amicable Number"

#59) deficientnum "Deficient Number"

#60) happynum "Happy Number"

#61) happyprime "Happy Prime"

#62) unhappynum "Unhappy Number"

#63) unhappyprime "Unhappy Prime"

#64) pseudoperfectnum "Pseudo-perfect Number"

#65) automorphicnum "Automorphic Number"

#66) duffiniannum "Duffinian Number"

#67) cuban1prime "Cuban 1 Prime"

#68) cuban2prime "Cuban 2 Prime"

#69) prothnum "Proth Number"

#70) prothprime "Proth Prime"

#71) wilsonprime "Wilson Prime"

#72) bellnum "Bell Number"

#73) bellprime "Bell Prime"

#74) carolnum "Carol Number"

#75) carolprime "Carol Prime"

#76) cdecagonalnum "Centered Decagonal Number"

#77) cdecagonalprime "Centered Decagonal Prime"

#78) cheptagonalnum "Centered Heptagonal Number"

#79) cheptagonalprime "Centered Heptagonal Prime"

#80) csquarenum "Centered Square Number"

#81) csquareprime "Centered Square Prime"

#82) ctriangularnum "Centered Triangular Number"

#83) ctriangularprime "Centered Triangular Prime"

#84) chenprime "Chen Prime"

#85) superprime "Super Prime"

#86) supersingularprime "Super Singular Prime"

#87) cullennum "Cullen Number"

#88) cullenprime "Cullen Prime"

#89) circularprime "Circular Prime"

#90) emirps "Reverse Primes (emirps)"

#91) primorialnum "Primorial Number"

#92) primorialprime "Primorial Prime"

#93) euclidnum "Euclid Number"

#94) euclidprime "Euclid Prime"

#95) evenprime "Even Prime"

#96) oddprime "Odd Prime"

#97) evennum "Even Number"

#98) oddnum "Odd Number"

#99) fermatnum "Fermat Number"

#100) fermatprime "Fermat Prime"

#101) genocchiprime "Genochi Prime"

#102) goodprime "Good Prime"

#103) kyneanum "Kynea Number"

#104) kyneaprime "Kynea Prime"

#105) lefttruncatableprime "Left Truncatable Prime"

#106) righttruncatableprime "Right Truncatable Prime"

#107) twosidedprime "Two Sided Prime"

#108) lucasnum "Lucas Number"

#109) lucasprime "Lucas Prime"

#110) minimalprime "Minimal Prime"

#111) padovannum "Padovan Number"

#112) padovanprime "Padovan Prime"

#113) partitionnum "Partition Number"

#114) partitionprime "Partition Prime"

#115) pellnum "Pell Number"

#116) pellprime "Pell Prime"

#117) perrinnum "Perrin Number"

#118) perrinprime "Perrin Prime"

#119) pierpontprime "Pierpont Prime"

#120) pythagoreanprime "Pythagorean Prime"

#121) binaryquadraticprime "Binary Quadratic Prime"

#122) quartanprime "Quartan Prime"

#123) residueclass6nplus1prime "Residue Class 6n + 1 Prime"

#124) residueclass6nplus5prime "Residue Class 6n + 5 Prime"

#125) residueclass8nplus1prime "Residue Class 8n + 1 Prime"

#126) residueclass8nplus3prime "Residue Class 8n + 3 Prime"

#127) residueclass8nplus5prime "Residue Class 8n + 5 Prime"

#128) residueclass8nplus7prime "Residue Class 8n + 7 Prime"

#129) residueclass10nplus1prime "Residue Class 10n + 1 Prime"

#130) residueclass10nplus3prime "Residue Class 10n + 3 Prime"

#131) residueclass10nplus7prime "Residue Class 10n + 7 Prime"

#132) residueclass10nplus9prime "Residue Class 10n + 9 Prime"

#133) safeprime "Safe Prime"

#134) sophiegermainprime "Sophie Germain Prime"

#135) starprime "Star Prime"

#136) thabitprime "Thabit Prime"

#137) wagstaffformprime "Wagstaff Form of (2p + 1) / 3 Prime"

#138) wagstaffvalueprime "Wagstaff Value p Prime"

#139) wieferichbase2prime "Wieferich base 2 prime"

#140) wieferichbase3prime "Wieferich base 3 prime"

#141) wieferichbase5prime "Wieferich base 5 prime"

#142) wieferichbase6prime "Wieferich base 6 prime"

#143) wieferichbase7prime "Wieferich base 7 prime"

#144) wieferichbase10prime "Wieferich base 10 prime"

#145) wieferichbase11prime "Wieferich base 11 prime"

#146) wieferichbase12prime "Wieferich base 12 prime"

#147) wieferichbase13prime "Wieferich base 13 prime"

#148) wieferichbase17prime "Wieferich base 17 prime"

#149) wieferichbase19prime "Wieferich base 19 prime"

#150) apocalypticpowernum "Apocalyptic Power Number"

#151) cakenum "Cake Number"

#152) catalannum "Catalan Number"

#153) compositorialnum "Compositorial Number"

#154) cubenum "Cube Number"

#155) evilnum "Evil Number"

#156) factorialnum "Factorial Number"

#157) odiousnum "Odious Number"

#158) lazycaterernum "Lazy Caterer Number"

#159) narcissisticnum "Narcissistic Number"

#160) powerof2num "Power of 2 Number"

#161) pronicnum "Pronic Number"

with(inttypes); # Loading the inttypes package

NyVJLWl0aGNvbXBvc2l0ZUc2IkktaXRocHJpbW9yaWFsR0YkSStwcmludHR5cGVzR0Yk

# Testing Function printtypes

# ================================

printtypes(1729);

UTFDb21wb3NpdGV+TnVtYmVyNiI=

US8zLUFsbW9zdH5QcmltZTYi

UTNTcXVhcmUtZnJlZX5OdW1iZXI2Ig==

UTFEZWZpY2llbnR+TnVtYmVyNiI=

US9VbmhhcHB5fk51bWJlcjYi

US1Qcm90aH5OdW1iZXI2Ig==

UStPZGR+TnVtYmVyNiI=

US5PZGlvdXN+TnVtYmVyNiI=

printtypes(3);

US1QcmltZX5OdW1iZXI2Ig==

UTBNZXJzZW5uZX5OdW1iZXI2Ig==

UThNZXJzZW5uZX5FeHBvbmVudH5QcmltZTYi

US9NZXJzZW5uZX5QcmltZTYi

UTFGaWJvbmFjY2l+TnVtYmVyNiI=

UTBGaWJvbmFjY2l+UHJpbWU2Ig==

UTFQZXJtdXRhYmxlflByaW1lNiI=

UTJMZXNzZXJ+VHdpbn5QcmltZTYi

UTRMZXNzZXJ+Q291c2luflByaW1lNiI=

US9HYXVzc2lhbn5QcmltZTYi

UTFSZXB+RGlnaXR+TnVtYmVyNiI=

UTNQYWxpbmRyb21pY35OdW1iZXI2Ig==

UTFCZWF1dGlmdWx+TnVtYmVyNiI=

UTJUcmlhbmd1bGFyfk51bWJlcjYi

UTNTcXVhcmUtZnJlZX5OdW1iZXI2Ig==

US1MdWNreX5OdW1iZXI2Ig==

USxMdWNreX5QcmltZTYi

UTFEZWZpY2llbnR+TnVtYmVyNiI=

US9VbmhhcHB5fk51bWJlcjYi

US5VbmhhcHB5flByaW1lNiI=

UTFEdWZmaW5pYW5+TnVtYmVyNiI=

US1Qcm90aH5OdW1iZXI2Ig==

USxQcm90aH5QcmltZTYi

UStDaGVuflByaW1lNiI=

UTVTdXBlcn5TaW5ndWxhcn5QcmltZTYi

US5DdWxsZW5+TnVtYmVyNiI=

US1DdWxsZW5+UHJpbWU2Ig==

US9DaXJjdWxhcn5QcmltZTYi

UTBQcmltb3JpYWx+UHJpbWU2Ig==

US5FdWNsaWR+TnVtYmVyNiI=

US1FdWNsaWR+UHJpbWU2Ig==

USpPZGR+UHJpbWU2Ig==

UStPZGR+TnVtYmVyNiI=

US5GZXJtYXR+TnVtYmVyNiI=

US1GZXJtYXR+UHJpbWU2Ig==

UTdMZWZ0flRydW5jYXRhYmxlflByaW1lNiI=

UThSaWdodH5UcnVuY2F0YWJsZX5QcmltZTYi

UTBUd29+U2lkZWR+UHJpbWU2Ig==

US1MdWNhc35OdW1iZXI2Ig==

USxMdWNhc35QcmltZTYi

US5NaW5pbWFsflByaW1lNiI=

US9QYWRvdmFufk51bWJlcjYi

US5QYWRvdmFuflByaW1lNiI=

UTFQYXJ0aXRpb25+TnVtYmVyNiI=

UTBQYXJ0aXRpb25+UHJpbWU2Ig==

US5QZXJyaW5+TnVtYmVyNiI=

US1QZXJyaW5+UHJpbWU2Ig==

US9QaWVycG9udH5QcmltZTYi

UTtSZXNpZHVlfkNsYXNzfjhufit+M35QcmltZTYi

UTxSZXNpZHVlfkNsYXNzfjEwbn4rfjN+UHJpbWU2Ig==

UTVTb3BoaWV+R2VybWFpbn5QcmltZTYi

USxTdXBlcn5QcmltZTYi

UURXYWdzdGFmZn5Gb3Jtfm9mfigycH4rfjEpfi9+M35QcmltZTYi

UTdXYWdzdGFmZn5WYWx1ZX5wflByaW1lNiI=

UThXaWVmZXJpY2h+YmFzZX4xMH5wcmltZTYi

UThXaWVmZXJpY2h+YmFzZX4xN35wcmltZTYi

UThXaWVmZXJpY2h+YmFzZX4xOX5wcmltZTYi

USxFdmlsfk51bWJlcjYi

UTROYXJjaXNzaXN0aWN+TnVtYmVyNiI=

# Testing Maple's ithprime function

# ==================================

ithprime(25);

IiMoKg==

ithprime(1);

IiIj

ithprime(2);

IiIk

ithprime(3);

IiIm

ithprime(5);

IiM2

ithprime(50);

IiRIIw==

# Testing function ithcomposite

# ================================

ithcomposite(25);

IiNR

ithcomposite(1);

IiIl

ithcomposite(2);

IiIn

ithcomposite(3);

IiIp

ithcomposite(5);

IiM1

ithcomposite(50);

IiNx

# Testing function ithprimorial

# ================================

ithprimorial(1);

IiIi

ithprimorial(2);

IiIj

ithprimorial(3);

IiIn

ithprimorial(4);

IiNJ

ithprimorial(5);

IiQ1Iw==

ithprimorial(6);

IiU1Qg==

# Testing Number Theory Types

# ============================================================================================================================

# Composite Number - Reference: http://oeis.org/A002808

# 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88

for i from 1 to 100 by 1 do

if type(i,compositenum) then printf("%d, ",i); end if;

end do;

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100,

# Prime: - Reference: http://oeis.org/A000040

# 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

for i from 1 to 300 by 1 do

if type(i,prime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293,

# Semiprime (2-almost prime): - Reference: http://oeis.org/A001358

# 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187

for i from 1 to 187 by 1 do

if type(i,semiprime) then printf("%d, ",i); end if;

end do;

4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187,

# 3-almost Prime: - Reference: http://oeis.org/A014612

# 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, 102, 105, 110, 114, 116, 117, 124, 125, 130, 138, 147, 148, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 195, 207, 212, 222, 230, 231, 236, 238, 242, 244

for i from 0 to 244 by 1 do

if type(i,almostprime3) then printf("%d, ",i); end if;

end do;

8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, 102, 105, 110, 114, 116, 117, 124, 125, 130, 138, 147, 148, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 195, 207, 212, 222, 230, 231, 236, 238, 242, 244,

# 4-almost Prime: - Reference: http://oeis.org/A014613

# 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376

for i from 0 to 376 by 1 do

if type(i,almostprime4) then printf("%d, ",i); end if;

end do;

16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376,

# 5-almost Prime: - Reference: http://oeis.org/A014614

# 32, 48, 72, 80, 108, 112, 120, 162, 168, 176, 180, 200, 208, 243, 252, 264, 270, 272, 280, 300, 304, 312, 368, 378, 392, 396, 405, 408, 420, 440, 450, 456, 464, 468, 496, 500, 520, 552, 567, 588, 592, 594, 612, 616, 630, 656, 660, 675, 680, 684, 688, 696

for i from 0 to 696 by 1 do

if type(i,almostprime5) then printf("%d, ",i); end if;

end do;

32, 48, 72, 80, 108, 112, 120, 162, 168, 176, 180, 200, 208, 243, 252, 264, 270, 272, 280, 300, 304, 312, 368, 378, 392, 396, 405, 408, 420, 440, 450, 456, 464, 468, 496, 500, 520, 552, 567, 588, 592, 594, 612, 616, 630, 656, 660, 675, 680, 684, 688, 696,

# 6-almost Prime: - Reference: http://oeis.org/A046306

# 64, 96, 144, 160, 216, 224, 240, 324, 336, 352, 360, 400, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040, 1104, 1134, 1176, 1184, 1188, 1215, 1224, 1232, 1260, 1312, 1320

for i from 0 to 1320 by 1 do

if type(i,almostprime6) then printf("%d, ",i); end if;

end do;

64, 96, 144, 160, 216, 224, 240, 324, 336, 352, 360, 400, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040, 1104, 1134, 1176, 1184, 1188, 1215, 1224, 1232, 1260, 1312, 1320,

# 7-almost Prime: - Reference: http://oeis.org/A046308

# 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832, 972, 1008, 1056, 1080, 1088, 1120, 1200, 1216, 1248, 1458, 1472, 1512, 1568, 1584, 1620, 1632, 1680, 1760, 1800, 1824, 1856, 1872, 1984, 2000, 2080, 2187, 2208, 2268, 2352, 2368, 2376

for i from 0 to 2376 by 1 do

if type(i,almostprime7) then printf("%d, ",i); end if;

end do;

128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832, 972, 1008, 1056, 1080, 1088, 1120, 1200, 1216, 1248, 1458, 1472, 1512, 1568, 1584, 1620, 1632, 1680, 1760, 1800, 1824, 1856, 1872, 1984, 2000, 2080, 2187, 2208, 2268, 2352, 2368, 2376,

# 8-almost Prime: - Reference: http://oeis.org/A046310

# 256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4160, 4374, 4416, 4536, 4704, 4736

for i from 0 to 4736 by 1 do

if type(i,almostprime8) then printf("%d, ",i); end if;

end do;

256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4160, 4374, 4416, 4536, 4704, 4736,

# 9-almost Prime: - Reference: http://oeis.org/A046312

# 512, 768, 1152, 1280, 1728, 1792, 1920, 2592, 2688, 2816, 2880, 3200, 3328, 3888, 4032, 4224, 4320, 4352, 4480, 4800, 4864, 4992, 5832, 5888, 6048, 6272, 6336, 6480, 6528, 6720, 7040, 7200, 7296, 7424, 7488, 7936, 8000, 8320, 8748, 8832, 9072, 9408

for i from 0 to 9408 by 1 do

if type(i,almostprime9) then printf("%d, ",i); end if;

end do;

512, 768, 1152, 1280, 1728, 1792, 1920, 2592, 2688, 2816, 2880, 3200, 3328, 3888, 4032, 4224, 4320, 4352, 4480, 4800, 4864, 4992, 5832, 5888, 6048, 6272, 6336, 6480, 6528, 6720, 7040, 7200, 7296, 7424, 7488, 7936, 8000, 8320, 8748, 8832, 9072, 9408,

# 10-almost Prime: - Reference: http://oeis.org/A046314

# 1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728, 9984, 11664, 11776, 12096, 12544, 12672, 12960, 13056, 13440, 14080, 14400, 14592, 14848, 14976, 15872, 16000, 16640

for i from 0 to 9728 by 1 do

if type(i,almostprime10) then printf("%d, ",i); end if;

end do;

1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728,

# 11-almost Prime: - Reference: http://oeis.org/A069272

# 2048, 3072, 4608, 5120, 6912, 7168, 7680, 10368, 10752, 11264, 11520, 12800, 13312, 15552, 16128, 16896, 17280, 17408, 17920, 19200, 19456, 19968, 23328, 23552, 24192, 25088, 25344, 25920, 26112, 26880, 28160, 28800, 29184, 29696

for i from 0 to 7680 by 1 do

if type(i,almostprime11) then printf("%d, ",i); end if;

end do;

2048, 3072, 4608, 5120, 6912, 7168, 7680,

# 12-almost Prime: - Reference: http://oeis.org/A069273

# 4096, 6144, 9216, 10240, 13824, 14336, 15360, 20736, 21504, 22528, 23040, 25600, 26624, 31104, 32256, 33792, 34560, 34816, 35840, 38400, 38912, 39936, 46656, 47104, 48384, 50176, 50688, 51840, 52224, 53760, 56320, 57600, 58368, 59392

for i from 0 to 13824 by 1 do

if type(i,almostprime12) then printf("%d, ",i); end if;

end do;

4096, 6144, 9216, 10240, 13824,

# 13-almost Prime: - Reference: http://oeis.org/A069274

# 8192, 12288, 18432, 20480, 27648, 28672, 30720, 41472, 43008, 45056, 46080, 51200, 53248, 62208, 64512, 67584, 69120, 69632, 71680, 76800, 77824, 79872, 93312, 94208, 96768, 100352, 101376, 103680, 104448, 107520, 112640, 115200

for i from 0 to 27648 by 1 do

if type(i,almostprime13) then printf("%d, ",i); end if;

end do;

8192, 12288, 18432, 20480, 27648,

# 14-almost Prime: - Reference: http://oeis.org/A069275

# 16384, 24576, 36864, 40960, 55296, 57344, 61440, 82944, 86016, 90112, 92160, 102400, 106496, 124416, 129024, 135168, 138240, 139264, 143360, 40960, 155648, 159744, 186624, 188416, 193536, 200704, 202752, 207360, 208896, 215040, 225280

for i from 0 to 55296 by 1 do

if type(i,almostprime14) then printf("%d, ",i); end if;

end do;

16384, 24576, 36864, 40960, 55296,

# 15-almost Prime: - Reference: http://oeis.org/A069276

# 32768, 49152, 73728, 81920, 110592, 114688, 122880, 165888, 172032, 180224, 184320, 204800, 212992, 248832, 258048, 270336, 276480, 278528, 286720, 307200, 311296, 319488, 373248, 376832, 387072, 401408, 405504, 414720, 417792, 430080

for i from 0 to 81920 by 1 do

if type(i,almostprime15) then printf("%d, ",i); end if;

end do;

32768, 49152, 73728, 81920,

# 16-almost Prime: - Reference: http://oeis.org/A069277

# 65536, 98304, 147456, 163840, 221184, 229376, 245760, 331776, 344064, 360448, 368640, 409600, 425984, 497664, 516096, 540672, 552960, 557056, 573440, 614400, 622592, 638976, 746496, 753664, 774144, 802816, 811008, 829440, 835584, 860160

for i from 0 to 163840 by 1 do

if type(i,almostprime16) then printf("%d, ",i); end if;

end do;

65536, 98304, 147456, 163840,

# 17-almost Prime: - Reference: http://oeis.org/A069278

# 131072, 196608, 294912, 327680, 442368, 458752, 491520, 663552, 688128, 720896, 737280, 819200, 851968, 995328, 1032192, 1081344, 1105920, 1114112, 1146880, 1228800, 1245184, 1277952, 1492992, 1507328, 1548288, 1605632, 1622016

if type(131072,almostprime17) then printf("%d, ",i); end if;

if type(196608,almostprime17) then printf("%d, ",i); end if;

if type(294912,almostprime17) then printf("%d, ",i); end if;

163841, 163841, 163841,

# 18-almost Prime: - Reference: http://oeis.org/A069279

# 262144, 393216, 589824, 655360, 884736, 917504, 983040, 1327104, 1376256, 1441792, 1474560, 1638400, 1703936, 1990656, 2064384, 2162688, 2211840, 2228224, 2293760, 2457600, 2490368, 2555904, 2985984, 3014656, 3096576

if type(262144,almostprime18) then printf("%d, ",i); end if;

if type(393216,almostprime18) then printf("%d, ",i); end if;

if type(589824,almostprime18) then printf("%d, ",i); end if;

163841, 163841, 163841,

# 19-almost Prime: - Reference: http://oeis.org/A069280

# 524288, 786432, 1179648, 1310720, 1769472, 1835008, 1966080, 2654208, 2752512, 2883584, 2949120, 3276800, 3407872, 3981312, 4128768, 4325376, 4423680, 4456448, 4587520, 4915200, 4980736, 5111808, 5971968, 6029312, 6193152

if type(524288,almostprime19) then printf("%d, ",i); end if;

if type(786432,almostprime19) then printf("%d, ",i); end if;

if type(1179648,almostprime19) then printf("%d, ",i); end if;

163841, 163841, 163841,

# 20-almost Prime: - Reference: http://oeis.org/A069281

# 1048576, 1572864, 2359296, 2621440, 3538944, 3670016, 3932160, 5308416, 5505024, 5767168, 5898240, 6553600, 6815744, 7962624, 8257536, 8650752, 8847360, 8912896, 9175040, 9830400, 9961472, 10223616, 11943936, 12058624

if type(1048576,almostprime20) then printf("%d, ",i); end if;

if type(1572864,almostprime20) then printf("%d, ",i); end if;

if type(2359296,almostprime20) then printf("%d, ",i); end if;

163841, 163841, 163841,

# Perfect Number: - Reference: http://oeis.org/A000396

# 6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128, 2658455991569831744654692615953842176, 191561942608236107294793378084303638130997321548169216

for i from 1 to 8128 by 1 do

if type(i,perfectnum) then printf("%d, ",i); end if;

end do;

6, 28, 496, 8128,

# Mersenne Number: - Reference: http://oeis.org/A000225

# 0, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647, 4294967295

for i from 0 to 16383 by 1 do

if type(i,mersennenum) then printf("%d, ",i); end if;

end do;

0, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383,

# Mersenne Prime: - Reference: http://oeis.org/A000668

# 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727

for i from 0 to 10000 by 1 do

if type(i,mersenneprime) then printf("%d, ",i); end if;

end do;

3, 7, 31, 127, 8191,

# Mersenne Exponent Prime: - Reference: http://oeis.org/A000043

# 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011

for i from 1 to 100000 by 1 do

if type(i,mersenneexpprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243,

# Fibonacci Number: - Reference: http://oeis.org/A000045

# 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169

for i from 0 to 10000 by 1 do

if type(i,fibonaccinum) then printf("%d, ",i); end if;

end do;

0, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765,

# Fibonacci Prime: - Reference: http://oeis.org/A005478

# 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376935476241

for i from 0 to 10000 by 1 do

if type(i,fibonacciprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 13, 89, 233, 1597,

# Permutable Prime: - Reference: http://oeis.org/A003459

# 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 199, 311, 337, 373, 733, 919, 991, 1111111111111111111, 11111111111111111111111

for i from 9 to 100 by 1 do

if type(i,permutableprime) then printf("%d, ",i); end if;

end do;

11, 13, 17, 31, 37, 71, 73, 79, 97,

# Lesser Twin Prime: - Reference: http://oeis.org/A001359

# 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607

for i from 0 to 2000 by 1 do

if type(i,lessertwinprime) then printf("%d, ",i); end if;

end do;

3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607, 1619, 1667, 1697, 1721, 1787, 1871, 1877, 1931, 1949, 1997,

# Greater Twin Prime: - Reference: http://oeis.org/A006512

# 5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609

for i from 0 to 2000 by 1 do

if type(i,greatertwinprime) then printf("%d, ",i); end if;

end do;

5, 7, 13, 19, 31, 43, 61, 73, 103, 109, 139, 151, 181, 193, 199, 229, 241, 271, 283, 313, 349, 421, 433, 463, 523, 571, 601, 619, 643, 661, 811, 823, 829, 859, 883, 1021, 1033, 1051, 1063, 1093, 1153, 1231, 1279, 1291, 1303, 1321, 1429, 1453, 1483, 1489, 1609, 1621, 1669, 1699, 1723, 1789, 1873, 1879, 1933, 1951, 1999,

# Lesser Cousin Prime: - Reference: http://oeis.org/A023200

# 3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429, 1447, 1483

for i from 0 to 1483 by 1 do

if type(i,lessercousinprime) then printf("%d, ",i); end if;

end do;

3, 7, 13, 19, 37, 43, 67, 79, 97, 103, 109, 127, 163, 193, 223, 229, 277, 307, 313, 349, 379, 397, 439, 457, 463, 487, 499, 613, 643, 673, 739, 757, 769, 823, 853, 859, 877, 883, 907, 937, 967, 1009, 1087, 1093, 1213, 1279, 1297, 1303, 1423, 1429, 1447, 1483,

# Greater Cousin Prime: - Reference: http://oeis.org/A046132

# 7, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353, 383, 401, 443, 461, 467, 491, 503, 617, 647, 677, 743, 761, 773, 827, 857, 863, 881, 887, 911, 941, 971, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433

for i from 0 to 1433 by 1 do

if type(i,greatercousinprime) then printf("%d, ",i); end if;

end do;

7, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353, 383, 401, 443, 461, 467, 491, 503, 617, 647, 677, 743, 761, 773, 827, 857, 863, 881, 887, 911, 941, 971, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433,

# Lesser Sexy Prime: - Reference: http://oeis.org/A023201

# 5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131, 151, 157, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 307, 311, 331, 347, 353, 367, 373, 383, 433, 443, 457, 461, 503, 541, 557, 563, 571, 587, 593, 601, 607, 613, 641, 647

for i from 0 to 647 by 1 do

if type(i,lessersexyprime) then printf("%d, ",i); end if;

end do;

5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 107, 131, 151, 157, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 307, 311, 331, 347, 353, 367, 373, 383, 433, 443, 457, 461, 503, 541, 557, 563, 571, 587, 593, 601, 607, 613, 641, 647,

# Greater Sexy Prime: - Reference: http://oeis.org/A046117

# 11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 89, 103, 107, 109, 113, 137, 157, 163, 173, 179, 197, 199, 229, 233, 239, 257, 263, 269, 277, 283, 313, 317, 337, 353, 359, 373, 379, 389, 439, 449, 463, 467, 509, 547, 563, 569, 577, 593, 599, 607, 613

for i from 0 to 613 by 1 do

if type(i,greatersexyprime) then printf("%d, ",i); end if;

end do;

11, 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 89, 103, 107, 109, 113, 137, 157, 163, 173, 179, 197, 199, 229, 233, 239, 257, 263, 269, 277, 283, 313, 317, 337, 353, 359, 373, 379, 389, 439, 449, 463, 467, 509, 547, 563, 569, 577, 593, 599, 607, 613,

# Eisenstein Prime: - Reference: http://oeis.org/A003627

# 2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569, 587

for i from 0 to 587 by 1 do

if type(i,eisensteinprime) then printf("%d, ",i); end if;

end do;

2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569, 587,

# Gaussian Prime: - Reference: http://oeis.org/A002145

# 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503, 523, 547, 563, 571

for i from 0 to 571 by 1 do

if type(i,gaussianprime) then printf("%d, ",i); end if;

end do;

3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 223, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503, 523, 547, 563, 571,

# Rep Digit Number: - Reference: http://oeis.org/A010785

# 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 111111, 222222

for i from 0 to 3333 by 1 do

if type(i,repdigitnum) then printf("%d, ",i); end if;

end do;

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 2222, 3333,

# Rep Unit Prime: - Reference: http://oeis.org/A004022

# 11, 1111111111111111111, 11111111111111111111111

type(11,repunitprime);

type(1111111111111111111,repunitprime);

type(11111111111111111111111,repunitprime);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

# Woodall Number: - Reference: http://oeis.org/A003261

# 1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519, 44040191, 92274687, 192937983, 402653183, 838860799, 1744830463, 3623878655, 7516192767

for i from 0 to 22527 by 1 do

if type(i,woodallnum) then printf("%d, ",i); end if;

end do;

1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527,

# Woodall Prime: - Reference: http://oeis.org/A050918

# 7, 23, 383, 32212254719, 2833419889721787128217599, 195845982777569926302400511, 4776913109852041418248056622882488319, 1307960347852357218937346147315859062783, 225251798594466661409915431774713195745814267044878909733007331390393510002687

for i from 0 to 500 by 1 do

if type(i,woodallprime) then printf("%d, ",i); end if;

end do;

7, 23, 383,

type(225251798594466661409915431774713195745814267044878909733007331390393510002687, woodallprime);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

# Palindromic Number: - Reference: http://oeis.org/A002113

# 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515

for i from 0 to 515 by 1 do

if type(i,palindromicnum) then printf("%d, ",i); end if;

end do;

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494, 505, 515,

JSFH

# Beautiful Number: - Reference: http://oeis.org/A032799

# 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175, 518, 598, 1306, 1676, 2427, 2646798, 12157692622039623539

for i from 0 to 2427 by 1 do

if type(i,beautifulnum) then printf("%d, ",i); end if;

end do;

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 89, 135, 175, 518, 598, 1306, 1676, 2427,

# Square Number: - Reference: http://oeis.org/A000290

# 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849

for i from 0 to 1849 by 1 do

if type(i,squarenum) then printf("%d, ",i); end if;

end do;

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849,

# Triangular Number: - Reference: http://oeis.org/A000217

# 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431

for i from 0 to 1431 by 1 do

if type(i,triangularnum) then printf("%d, ",i); end if;

end do;

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431,

# Oblong Number: - Reference: http://oeis.org/A002378

# 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550

for i from 0 to 2550 by 1 do

if type(i,oblongnum) then printf("%d, ",i); end if;

end do;

0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550,

# Hexagonal Number: - Reference: http://oeis.org/A000384

# 0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, 3003, 3160, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4560

for i from 0 to 4560 by 1 do

if type(i,hexagonalnum) then printf("%d, ",i); end if;

end do;

0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, 3003, 3160, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4560,

# Tetrahedral Number: - Reference: http://oeis.org/A000292

# 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180

for i from 0 to 15180 by 1 do

if type(i,tetrahedralnum) then printf("%d, ",i); end if;

end do;

0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, 455, 560, 680, 816, 969, 1140, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180,

# Decagonal Number: - Reference: http://oeis.org/A001107

# 0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326

for i from 0 to 8326 by 1 do

if type(i,decagonalnum) then printf("%d, ",i); end if;

end do;

0, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 4000, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326,

# Abundant Number: - Reference: http://oeis.org/A005101

# 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264, 270

for i from 0 to 270 by 1 do

if type(i,abundantnum) then printf("%d, ",i); end if;

end do;

12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264, 270,

# Aspiring Number: - Reference: http://oeis.org/A063769

# 25, 95, 119, 143, 417, 445, 565, 608, 650, 652, 675, 685

for i from 0 to 685 by 1 do

if type(i,aspiringnum) then printf("%d, ",i); end if;

end do;

25, 95, 119, 143, 417, 445, 565, 608, 650, 652, 675, 685,

# Sociable Number: - Reference: http://oeis.org/A122726

# 12496, 14264, 14288, 14316, 14536, 15472, 17716, 19116, 19916, 22744, 22976, 31704, 45946, 47616, 48976, 83328, 97946, 122410, 152990, 177792, 243760, 274924, 275444, 285778, 294896, 295488, 358336, 366556, 376736, 381028, 418904, 589786

for i from 1 to 31704 by 1 do

if type(i, sociablenum) then printf("%d, ",i); end if;

end do;

12496, 14264, 14288, 14316, 14536, 15472, 17716, 19116, 19916, 22744, 22976, 31704,

# Apocalyptic Power Number: - Reference: http://oeis.org/A007356

# 157, 192, 218, 220, 222, 224, 226, 243, 245, 247, 251, 278, 285, 286, 287, 312, 355, 361, 366, 382, 384, 390, 394, 411, 434, 443, 478, 497, 499, 506, 508, 528, 529, 539, 540, 541, 564, 578, 580, 582, 583, 610

for i from 1 to 610 by 1 do

if type(i, apocalypticpowernum) then printf("%d, ",i); end if;

end do;

157, 192, 218, 220, 222, 224, 226, 243, 245, 247, 251, 278, 285, 286, 287, 312, 355, 361, 366, 382, 384, 390, 394, 411, 434, 443, 478, 497, 499, 506, 508, 528, 529, 539, 540, 541, 564, 578, 580, 582, 583, 610,

# Cake Number: - Reference: http://oeis.org/A000125

# 1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697, 834, 988, 1160, 1351, 1562, 1794, 2048, 2325, 2626, 2952, 3304, 3683, 4090, 4526, 4992, 5489, 6018, 6580, 7176, 7807, 8474, 9178, 9920, 10701, 11522, 12384, 13288, 14235, 15226

for i from 0 to 15300 by 1 do

if type(i, cakenum) then printf("%d, ",i); end if;

end do;

1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697, 834, 988, 1160, 1351, 1562, 1794, 2048, 2325, 2626, 2952, 3304, 3683, 4090, 4526, 4992, 5489, 6018, 6580, 7176, 7807, 8474, 9178, 9920, 10701, 11522, 12384, 13288, 14235, 15226,

# Catalan Number: - Reference: http://oeis.org/A000108

# 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004, 263747951750360, 1002242216651368, 3814986502092304

for i from 0 to 58786 by 1 do

if type(i, catalannum) then printf("%d, ",i); end if;

end do;

1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786,

# Compositorial Number: - Reference: http://oeis.org/A036691

# 1, 4, 24, 192, 1728, 17280, 207360, 2903040, 43545600, 696729600, 12541132800, 250822656000, 5267275776000, 115880067072000, 2781121609728000, 69528040243200000, 1807729046323200000, 48808684250726400000, 1366643159020339200000

for i from 1 to 207360 by 1 do

if type(i, compositorialnum) then printf("%d, ",i); end if;

end do;

1, 4, 24, 192, 1728, 17280, 207360,

# Cube Number: - Reference: http://oeis.org/A000578

# 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000

for i from 0 to 64000 by 1 do

if type(i, cubenum) then printf("%d, ",i); end if;

end do;

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000,

# Automorphicnum Number (Curious Number): - Reference: http://oeis.org/A003226

# 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625, 87109376, 212890625, 787109376, 1787109376, 8212890625, 18212890625, 81787109376, 918212890625, 9918212890625, 40081787109376, 59918212890625

for i from 0 to 90625 by 1 do

if type(i, automorphicnum) then printf("%d, ",i); end if;

end do;

0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625,

# Evil Number: - Reference: http://oeis.org/A001969

# 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 63, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 95, 96, 99, 101, 102, 105, 106, 108, 111, 113, 114, 116, 119, 120, 123, 125, 126, 129

for i from 0 to 129 by 1 do

if type(i, evilnum) then printf("%d, ",i); end if;

end do;

0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 63, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 95, 96, 99, 101, 102, 105, 106, 108, 111, 113, 114, 116, 119, 120, 123, 125, 126, 129,

# Odious Number: - Reference: http://oeis.org/A000069

# 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 64, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 97, 98, 100, 103, 104, 107, 109, 110, 112, 115, 117, 118, 121, 122, 124, 127, 128

for i from 0 to 129 by 1 do

if type(i, odiousnum) then printf("%d, ",i); end if;

end do;

1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 64, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 97, 98, 100, 103, 104, 107, 109, 110, 112, 115, 117, 118, 121, 122, 124, 127, 128,

# Factorial Number: - Reference: http://oeis.org/A000142

# 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600, 6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000, 6402373705728000, 121645100408832000, 2432902008176640000

for i from 0 to 40320 by 1 do

if type(i, factorialnum) then printf("%d, ",i); end if;

end do;

1, 2, 6, 24, 120, 720, 5040, 40320,

# Lazy Caterer Number: - Reference: http://oeis.org/A000124

# 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379

for i from 0 to 1379 by 1 do

if type(i, lazycaterernum) then printf("%d, ",i); end if;

end do;

1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, 232, 254, 277, 301, 326, 352, 379, 407, 436, 466, 497, 529, 562, 596, 631, 667, 704, 742, 781, 821, 862, 904, 947, 991, 1036, 1082, 1129, 1177, 1226, 1276, 1327, 1379,

# Narcissistic Number (Plus Perfect Number): - Reference: http://oeis.org/A005188

# 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315, 24678050, 24678051, 88593477, 146511208, 472335975, 534494836, 912985153, 4679307774, 32164049650, 32164049651

for i from 0 to 93084 by 1 do

if type(i, narcissisticnum) then printf("%d, ",i); end if;

end do;

1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084,

# Power of 2 Number: - Reference: http://oeis.org/A000079

# 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592

for i from 0 to 32768 by 1 do

if type(i, powerof2num) then printf("%d, ",i); end if;

end do;

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768,

# Pronic Number (Heteromecic Number): - Reference: http://oeis.org/A002378

for i from 0 to 2550 by 1 do

if type(i, pronicnum) then printf("%d, ",i); end if;

end do;

# Square-free Number: - Reference: http://oeis.org/A005117

# 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113

for i from 0 to 113 by 1 do

if type(i, squarefreenum) then printf("%d, ",i); end if;

end do;

0, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113,

# Lucky Number: - Reference: http://oeis.org/A000959

# 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303

for i from 0 to 303 by 1 do

if type(i, luckynum) then printf("%d, ",i); end if;

end do;

1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303,

# Lucky Prime: - Reference: http://oeis.org/A031157

# 3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123

for i from 0 to 1123 by 1 do

if type(i, luckyprime) then printf("%d, ",i); end if;

end do;

3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123,

# Pentagonal Number: - Reference: http://oeis.org/A000326

# 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151

for i from 0 to 3151 by 1 do

if type(i, pentagonalnum) then printf("%d, ",i); end if;

end do;

0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151,

# Amicable Number: - Reference: http://oeis.org/A063990

# 220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 67095, 69615, 71145, 76084, 79750, 87633, 88730, 100485, 122265, 122368, 123152, 124155, 139815, 141664, 142310

for i from 0 to 67095 by 1 do

if type(i, amicablenum) then printf("%d, ",i); end if;

end do;

220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 67095,

# Deficient Number: - Reference: http://oeis.org/A005100

# 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86

for i from 0 to 86 by 1 do

if type(i, deficientnum) then printf("%d, ",i); end if;

end do;

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 82, 83, 85, 86,

# Happy Number: - Reference: http://oeis.org/A007770

# 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338

for i from 0 to 338 by 1 do

if type(i, happynum) then printf("%d, ",i); end if;

end do;

1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338,

# Happy Prime: - Reference: http://oeis.org/A035497

# 7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093, 1151, 1277, 1303, 1373, 1427, 1447, 1481, 1487, 1511, 1607, 1663

for i from 0 to 1663 by 1 do

if type(i, happyprime) then printf("%d, ",i); end if;

end do;

7, 13, 19, 23, 31, 79, 97, 103, 109, 139, 167, 193, 239, 263, 293, 313, 331, 367, 379, 383, 397, 409, 487, 563, 617, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1009, 1033, 1039, 1093, 1151, 1277, 1303, 1373, 1427, 1447, 1481, 1487, 1511, 1607, 1663,

# Unhappy Number: - Reference: http://oeis.org/A031177

# 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81

for i from 0 to 81 by 1 do

if type(i, unhappynum) then printf("%d, ",i); end if;

end do;

2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81,

# Unhappy Prime: - Reference: http://oeis.org/A094480

# 2, 3, 5, 11, 17, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 101, 107, 113, 127, 131, 137, 149, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 269, 271, 277, 281, 283, 307, 311, 317, 337, 347, 349, 353, 359, 373

for i from 0 to 373 by 1 do

if type(i, unhappyprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 11, 17, 29, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 83, 89, 101, 107, 113, 127, 131, 137, 149, 151, 157, 163, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 241, 251, 257, 269, 271, 277, 281, 283, 307, 311, 317, 337, 347, 349, 353, 359, 373,

# Pseudo-perfect Number: - Reference: http://oeis.org/A005835

# 6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264

for i from 0 to 234 by 1 do

if type(i, pseudoperfectnum) then printf("%d, ",i); end if;

end do;

6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234,

# Duffinian Number: - Reference: http://oeis.org/A014567

# 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 36, 37, 39, 41, 43, 47, 49, 50, 53, 55, 57, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 89, 93, 97, 98, 100, 101, 103, 107, 109, 111, 113, 115, 119, 121, 125, 127, 128, 129, 131, 133

for i from 0 to 133 by 1 do

if type(i, duffiniannum) then printf("%d, ",i); end if;

end do;

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 36, 37, 39, 41, 43, 47, 49, 50, 53, 55, 57, 59, 61, 63, 64, 65, 67, 71, 73, 75, 77, 79, 81, 83, 85, 89, 93, 97, 98, 100, 101, 103, 107, 109, 111, 113, 115, 119, 121, 125, 127, 128, 129, 131, 133,

# Cuban 1 Prime: - Reference: http://oeis.org/A002407

# 7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211, 7057, 7351, 8269, 9241, 10267, 11719, 12097, 13267, 13669, 16651, 19441, 19927, 22447, 23497, 24571, 25117, 26227

for i from 0 to 6211 by 1 do

if type(i, cuban1prime) then printf("%d, ",i); end if;

end do;

7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, 3571, 4219, 4447, 5167, 5419, 6211,

# Cuban 2 Prime: - Reference: http://oeis.org/A002648

# 13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201, 47629, 60493, 63949, 65713, 69313, 73009, 76801, 84673, 106033, 108301, 112909, 115249, 129793, 139969

for i from 0 to 43201 by 1 do

if type(i, cuban2prime) then printf("%d, ",i); end if;

end do;

13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, 43201,

# Proth Number: - Reference: http://oeis.org/A080075

# 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1025, 1089, 1153, 1217, 1281, 1345, 1409

for i from 0 to 1409 by 1 do

if type(i, prothnum) then printf("%d, ",i); end if;

end do;

3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, 81, 97, 113, 129, 145, 161, 177, 193, 209, 225, 241, 257, 289, 321, 353, 385, 417, 449, 481, 513, 545, 577, 609, 641, 673, 705, 737, 769, 801, 833, 865, 897, 929, 961, 993, 1025, 1089, 1153, 1217, 1281, 1345, 1409,

# Proth Prime: - Reference: http://oeis.org/A080076

# 3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857, 10369, 10753, 11393, 11777, 12161, 12289, 13313

for i from 0 to 13313 by 1 do

if type(i, prothprime) then printf("%d, ",i); end if;

end do;

3, 5, 13, 17, 41, 97, 113, 193, 241, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1409, 1601, 2113, 2689, 2753, 3137, 3329, 3457, 4481, 4993, 6529, 7297, 7681, 7937, 9473, 9601, 9857, 10369, 10753, 11393, 11777, 12161, 12289, 13313,

# Wilson Prime: - Reference: http://oeis.org/A007540

# 5, 13, 563

for i from 0 to 1000 by 1 do

if type(i, wilsonprime) then printf("%d, ",i); end if;

end do;

5, 13, 563,

# Bell Number: - Reference: http://oeis.org/A000110

# 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346

for i from 0 to 21147 by 1 do

if type(i, bellnum) then printf("%d, ",i); end if;

end do;

1, 2, 5, 15, 52, 203, 877, 4140, 21147,

# Bell Prime: - Reference: http://oeis.org/A051131

# 2, 5, 877, 27644437, 35742549198872617291353508656626642567, 359334085968622831041960188598043661065388726959079837

for i from 0 to 877 by 1 do

if type(i, bellprime) then printf("%d, ",i); end if;

end do;

2, 5, 877,

# Carol Number: - Reference: http://oeis.org/A093112

# -1, 7, 47, 223, 959, 3967, 16127, 65023, 261119, 1046527, 4190207, 16769023, 67092479, 268402687, 1073676287, 4294836223, 17179607039, 68718952447, 274876858367, 1099509530623, 4398042316799, 17592177655807

for i from -50 to 16127 by 1 do

if type(i, carolnum) then printf("%d, ",i); end if;

end do;

-1, 7, 47, 223, 959, 3967, 16127,

# Carol Prime: - Reference: http://oeis.org/A091516

# 7, 47, 223, 3967, 16127, 1046527, 16769023, 1073676287, 68718952447, 274876858367, 4398042316799, 1125899839733759, 18014398241046527, 1298074214633706835075030044377087

for i from -50 to 261119 by 1 do

if type(i,carolprime) then printf("%d, ",i); end if;

end do;

7, 47, 223, 3967, 16127,

# Centered Decagonal Number: - Reference: http://oeis.org/A062786

# 1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901

for i from 0 to 9901 by 1 do

if type(i,cdecagonalnum) then printf("%d, ",i); end if;

end do;

1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, 1201, 1361, 1531, 1711, 1901, 2101, 2311, 2531, 2761, 3001, 3251, 3511, 3781, 4061, 4351, 4651, 4961, 5281, 5611, 5951, 6301, 6661, 7031, 7411, 7801, 8201, 8611, 9031, 9461, 9901,

# Centered Decagonal Prime: - Reference: http://oeis.org/A090562

# 11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1531, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281, 6301, 6661, 7411, 9461, 9901, 12251, 13781, 14851, 15401, 18301, 18911, 19531, 20161, 22111, 24151, 24851, 25561, 27011, 27751

for i from 0 to 27751 by 1 do

if type(i,cdecagonalprime) then printf("%d, ",i); end if;

end do;

11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1531, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281, 6301, 6661, 7411, 9461, 9901, 12251, 13781, 14851, 15401, 18301, 18911, 19531, 20161, 22111, 24151, 24851, 25561, 27011, 27751,

# Centered Heptagonal Number: - Reference: http://oeis.org/A069099

# 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331, 1471, 1618, 1772, 1933, 2101, 2276, 2458, 2647, 2843, 3046, 3256, 3473, 3697, 3928, 4166, 4411, 4663, 4922, 5188, 5461, 5741, 6028, 6322, 6623, 6931, 7246

for i from 0 to 7246 by 1 do

if type(i,cheptagonalnum) then printf("%d, ",i); end if;

end do;

1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953, 1072, 1198, 1331, 1471, 1618, 1772, 1933, 2101, 2276, 2458, 2647, 2843, 3046, 3256, 3473, 3697, 3928, 4166, 4411, 4663, 4922, 5188, 5461, 5741, 6028, 6322, 6623, 6931, 7246,

# Centered Heptagonal Prime: - Reference: http://oeis.org/A144974

# 43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, 4663, 5741, 8233, 9283, 10781, 11173, 12391, 14561, 18397, 20483, 29303, 29947, 34651, 37493, 41203, 46691, 50821, 54251, 56897, 57793, 65213, 68111, 72073, 76147, 84631, 89041

for i from 0 to 89041 by 1 do

if type(i,cheptagonalprime) then printf("%d, ",i); end if;

end do;

43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, 4663, 5741, 8233, 9283, 10781, 11173, 12391, 14561, 18397, 20483, 29303, 29947, 34651, 37493, 41203, 46691, 50821, 54251, 56897, 57793, 65213, 68111, 72073, 76147, 84631, 89041,

# Centered Square Number: - Reference: http://oeis.org/A001844

# 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325

for i from 0 to 4325 by 1 do

if type(i,csquarenum) then printf("%d, ",i); end if;

end do;

1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325,

# Centered Square Prime: - Reference: http://oeis.org/A027862

# 5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613, 4513, 5101, 7321, 8581, 9661, 9941, 10513, 12641, 13613, 14281, 14621, 15313, 16381, 19013, 19801, 20201, 21013, 21841, 23981, 24421, 26681

for i from 0 to 26681 by 1 do

if type(i,csquareprime) then printf("%d, ",i); end if;

end do;

5, 13, 41, 61, 113, 181, 313, 421, 613, 761, 1013, 1201, 1301, 1741, 1861, 2113, 2381, 2521, 3121, 3613, 4513, 5101, 7321, 8581, 9661, 9941, 10513, 12641, 13613, 14281, 14621, 15313, 16381, 19013, 19801, 20201, 21013, 21841, 23981, 24421, 26681,

# Centered Triangular Number: - Reference: http://oeis.org/A144974

# 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2584, 2710, 2839, 2971, 3106, 3244, 3385, 3529

for i from 0 to 3529 by 1 do

if type(i,ctriangularnum) then printf("%d, ",i); end if;

end do;

1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, 235, 274, 316, 361, 409, 460, 514, 571, 631, 694, 760, 829, 901, 976, 1054, 1135, 1219, 1306, 1396, 1489, 1585, 1684, 1786, 1891, 1999, 2110, 2224, 2341, 2461, 2584, 2710, 2839, 2971, 3106, 3244, 3385, 3529,

# Centered Triangular Prime: - Reference: http://oeis.org/A125602

# 19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971, 3529, 4621, 4789, 7039, 7669, 8779, 9721, 10459, 10711, 13681, 14851, 16069, 16381, 17659, 20011, 20359, 23251, 25939, 27541, 29191, 29611, 31321, 34429, 36739, 40099, 40591, 42589

for i from 0 to 42589 by 1 do

if type(i,ctriangularprime) then printf("%d, ",i); end if;

end do;

19, 31, 109, 199, 409, 571, 631, 829, 1489, 1999, 2341, 2971, 3529, 4621, 4789, 7039, 7669, 8779, 9721, 10459, 10711, 13681, 14851, 16069, 16381, 17659, 20011, 20359, 23251, 25939, 27541, 29191, 29611, 31321, 34429, 36739, 40099, 40591, 42589,

# Chen Prime: - Reference: http://oeis.org/A109611

# 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409

for i from 0 to 409 by 1 do

if type(i,chenprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409,

# Super Prime: - Reference: http://oeis.org/A006450

# 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, 1031, 1063, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1433, 1447, 1471

for i from 0 to 1471 by 1 do

if type(i,superprime) then printf("%d, ",i); end if;

end do;

3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, 1031, 1063, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1433, 1447, 1471,

# Super Singular Prime: - Reference: http://oeis.org/A002267

# 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71

for i from 0 to 100 by 1 do

if type(i,supersingularprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71,

# Cullen Number: - Reference: http://oeis.org/A002064

# 1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521, 44040193, 92274689, 192937985, 402653185, 838860801, 1744830465, 3623878657, 7516192769, 15569256449, 32212254721

for i from 0 to 49153 by 1 do

if type(i,cullennum) then printf("%d, ",i); end if;

end do;

1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153,

# Cullen Prime: - Reference: http://oeis.org/A050920

# 3, 393050634124102232869567034555427371542904833

for i from 0 to 1000 by 1 do

if type(i,cullenprime) then printf("%d, ",i); end if;

end do;

type(393050634124102232869567034555427371542904833, cullenprime);

SSV0cnVlRyUqcHJvdGVjdGVkRw==

# Circular Prime: - Reference: http://oeis.org/A068652

# 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993

for i from 0 to 3119 by 1 do

if type(i,circularprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119,

# Reverse Primes (emirps): - Reference: http://oeis.org/A006567

# 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193

for i from 0 to 1193 by 1 do

if type(i,emirps) then printf("%d, ",i); end if;

end do;

13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193,

# Primorial Number: - Reference: http://oeis.org/A002064

# 1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070

for i from 0 to 30030 by 1 do

if type(i,primorialnum) then printf("%d, ",i); end if;

end do;

1, 2, 6, 30, 210, 2310, 30030,

# Primorial Prime: - Reference: http://oeis.org/A057705 union http://oeis.org/A018239

# 3, 5, 7, 29, 31, 211, 2309, 2311, 30029, 200560490131, 304250263527209, 23768741896345550770650537601358309

for i from 0 to 30029 by 1 do

if type(i,primorialprime) then printf("%d, ",i); end if;

end do;

3, 5, 7, 29, 31, 211, 2309, 2311, 30029,

# Euclid Number: - Reference: http://oeis.org/A006862 minus {2}

# 3, 7, 31, 211, 2311, 30031, 510511, 9699691, 223092871, 6469693231, 200560490131, 7420738134811, 304250263527211, 13082761331670031, 614889782588491411, 32589158477190044731, 1922760350154212639071

for i from 0 to 30031 by 1 do

if type(i,euclidnum) then printf("%d, ",i); end if;

end do;

3, 7, 31, 211, 2311, 30031,

# Euclid Prime: - Reference: http://oeis.org/A018239 minus {2}

# 3, 7, 31, 211, 2311, 200560490131,

for i from 0 to 2311 by 1 do

if type(i,euclidprime) then printf("%d, ",i); end if;

end do;

3, 7, 31, 211, 2311,

# Even Number: - Reference:http://oeis.org/A005843

# 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120

for i from 0 to 120 by 1 do

if type(i,evennum) then printf("%d, ",i); end if;

end do;

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120,

# Odd Number: - Reference: http://oeis.org/A005408

# 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131

for i from 0 to 131 by 1 do

if type(i,oddnum) then printf("%d, ",i); end if;

end do;

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131,

# Even Prime: - Reference: (The only even prime is 2)

# 2

for i from 0 to 300 by 1 do

if type(i,evenprime) then printf("%d, ",i); end if;

end do;

# Odd Prime: - Reference: http://oeis.org/A065091

# 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

for i from 0 to 271 by 1 do

if type(i,oddprime) then printf("%d, ",i); end if;

end do;

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271,

# Fermat Number: - Reference: http://oeis.org/A000215

# 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, 340282366920938463463374607431768211457

for i from 0 to 65537 by 1 do

if type(i,fermatnum) then printf("%d, ",i); end if;

end do;

3, 5, 17, 257, 65537,

# Fermat Prime: - Reference: http://oeis.org/A019434

# 3, 5, 17, 257, 65537

for i from 0 to 65537 by 1 do

if type(i,fermatprime) then printf("%d, ",i); end if;

end do;

3, 5, 17, 257, 65537,

# Genochi Prime: - Reference: (The only positive prime Genocchi number is 17)

for i from 0 to 271 by 1 do

if type(i,genocchiprime) then printf("%d, ",i); end if;

end do;

17,

# Good Prime: - Reference: http://oeis.org/A028388

# 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307, 311, 331, 347, 419, 431, 541, 557, 563, 569, 587, 593, 599, 641, 727, 733, 739, 809, 821, 853, 929, 937, 967, 1009, 1031, 1087, 1151, 1213, 1277

for i from 1 to 541 by 1 do

if type(i,goodprime) then printf("%d, ",i); end if;

end do;

5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307, 311, 331, 347, 419, 431, 541,

# Kynea Number: - Reference: http://oeis.org/A093069

# 7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247, 268468223, 1073807359, 4295098367, 17180131327, 68720001023, 274878955519, 1099513724927, 4398050705407, 17592194433023

for i from 0 to 66047 by 1 do

if type(i,kyneanum) then printf("%d, ",i); end if;

end do;

7, 23, 79, 287, 1087, 4223, 16639, 66047,

# Kynea Prime: - Reference: http://oeis.org/A091514

# 7, 23, 79, 1087, 66047, 263167, 16785407, 1073807359, 17180131327, 68720001023, 4398050705407, 70368760954879, 18014398777917439, 18446744082299486207, 5070602400912922109586440191999

for i from 0 to 66047 by 1 do

if type(i,kyneaprime) then printf("%d, ",i); end if;

end do;

7, 23, 79, 1087, 66047,

# Left Truncatable Prime: - Reference: http://oeis.org/A028388

# 2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 937, 947, 953, 967, 983, 997, 1223

for i from 0 to 1223 by 1 do

if type(i,lefttruncatableprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, 223, 283, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 523, 547, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 937, 947, 953, 967, 983, 997, 1223,

# Right Truncatable Prime: - Reference: http://oeis.org/A024770

# 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393, 23333, 23339, 23399, 23993, 29399, 31193

for i from 0 to 31193 by 1 do

if type(i,righttruncatableprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393, 23333, 23339, 23399, 23993, 29399, 31193,

# Two Sided Prime: - Reference: http://oeis.org/A020994

# 2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397

for i from 0 to 3797 by 1 do

if type(i,twosidedprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797,

# Lucas Number: - Reference: http://oeis.org/A000032

# 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282

for i from 3 to 9349 by 1 do

if type(i,lucasnum) then printf("%d, ",i); end if;

end do;

3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349,

type(0,lucasnum); # 2 if i = 0

SSV0cnVlRyUqcHJvdGVjdGVkRw==

type(1,lucasnum); # 1 if i = 1

SSV0cnVlRyUqcHJvdGVjdGVkRw==

# L[i-1] + L[i-2] if i > 1

# Lucas Prime: - Reference: http://oeis.org/A005479

# 2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349, 3010349, 54018521, 370248451, 6643838879, 119218851371, 5600748293801, 688846502588399, 32361122672259149, 412670427844921037470771

for i from 0 to 9349 by 1 do

if type(i,lucasprime) then printf("%d, ",i); end if;

end do;

2, 3, 7, 11, 29, 47, 199, 521, 2207, 3571, 9349,

# Minimal Prime: - Reference: http://oeis.org/A071062

# 2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049

for i from 0 to 9949 by 1 do

if type(i,minimalprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949,

# Padovan Number: - Reference: http://oeis.org/A000931

# 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625

for i from 0 to 1432 by 1 do

if type(i,padovannum) then printf("%d, ",i); end if;

end do;

1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432,

# Padovan Prime: - Reference: http://oeis.org/A100891

# 2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719

for i from 0 to 3329 by 1 do

if type(i,padovanprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 37, 151, 3329,

# Partition Number: - Reference: http://oeis.org/A000041

# 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134

for i from 0 to 89134 by 1 do

if type(i,partitionnum) then printf("%d, ",i); end if;

end do;

1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1958, 2436, 3010, 3718, 4565, 5604, 6842, 8349, 10143, 12310, 14883, 17977, 21637, 26015, 31185, 37338, 44583, 53174, 63261, 75175, 89134,

# Partition Prime: - Reference: http://oeis.org/A049575

# 2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557

for i from 0 to 17977 by 1 do

if type(i,partitionprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 11, 101, 17977,

# Pell Number: - Reference: http://oeis.org/A000129

# 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, 33461, 80782, 195025, 470832, 1136689, 2744210, 6625109, 15994428, 38613965, 93222358, 225058681, 543339720, 1311738121, 3166815962, 7645370045, 18457556052, 44560482149

for i from 0 to 5741 by 1 do

if type(i,pellnum) then printf("%d, ",i); end if;

end do;

0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741,

# Pell Prime: - Reference: http://oeis.org/A086383

# 2, 5, 29, 5741, 33461, 44560482149, 1746860020068409, 68480406462161287469, 13558774610046711780701, 4125636888562548868221559797461449, 4760981394323203445293052612223893281

for i from 0 to 33461 by 1 do

if type(i,pellprime) then printf("%d, ",i); end if;

end do;

2, 5, 29, 5741, 33461,

# Perrin Number: - Reference: http://oeis.org/A001608

# 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, 486, 644, 853, 1130, 1497, 1983, 2627, 3480, 4610, 6107, 8090, 10717, 14197, 18807, 24914, 33004, 43721, 57918, 76725, 101639, 134643, 178364, 236282, 313007

for i from 0 to 3480 by 1 do

if type(i,perrinnum) then printf("%d, ",i); end if;

end do;

0, 2, 3, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, 486, 644, 853, 1130, 1497, 1983, 2627, 3480,

# Perrin Prime: - Reference: http://oeis.org/A074788

# 2, 3, 5, 7, 17, 29, 277, 367, 853, 14197, 43721, 1442968193, 792606555396977, 187278659180417234321, 66241160488780141071579864797,

for i from 0 to 14197 by 1 do

if type(i,perrinprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 17, 29, 277, 367, 853, 14197,

# Pierpont Prime: - Reference: http://oeis.org/A005109

# 2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433, 487, 577, 769, 1153, 1297, 1459, 2593, 2917, 3457, 3889, 10369, 12289, 17497, 18433, 39367, 52489, 65537, 139969, 147457, 209953, 331777, 472393, 629857, 746497, 786433, 839809, 995329

for i from 0 to 433 by 1 do

if type(i,pierpontprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 7, 13, 17, 19, 37, 73, 97, 109, 163, 193, 257, 433,

# Pythagorean Prime: - Reference: http://oeis.org/A002144

# 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397, 401, 409, 421, 433, 449, 457, 461, 509, 521, 541, 557, 569, 577, 593, 601, 613, 617

for i from 0 to 281 by 1 do

if type(i,pythagoreanprime) then printf("%d, ",i); end if;

end do;

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281,

# Binary Quadratic Prime: - Reference: http://oeis.org/A106856

# 2, 11, 23, 37, 43, 53, 71, 79, 107, 109, 127, 137, 149, 151, 163, 193, 197, 211, 233, 239, 263, 281, 317, 331, 337, 373, 389, 401, 421, 431, 443, 463, 487, 491, 499, 541, 547, 557, 569, 599, 613, 617, 641, 653, 659, 673, 683, 739, 743, 751, 757, 809, 821

for i from 0 to 401 by 1 do

if type(i,binaryquadraticprime) then printf("%d, ",i); end if;

end do;

2, 11, 23, 37, 43, 53, 71, 79, 107, 109, 127, 137, 149, 151, 163, 193, 197, 211, 233, 239, 263, 281, 317, 331, 337, 373, 389, 401,

# Quartan Prime: - Reference: http://oeis.org/A002645

# 2, 17, 97, 257, 337, 641, 881, 1297, 2417, 2657, 3697, 4177, 4721, 6577, 10657, 12401, 14657, 14897, 15937, 16561, 28817, 38561, 39041, 49297, 54721, 65537, 65617, 66161, 66977, 80177, 83537, 83777, 89041, 105601, 107377, 119617, 121937

for i from 0 to 1297 by 1 do

if type(i,quartanprime) then printf("%d, ",i); end if;

end do;

2, 17, 97, 257, 337, 641, 881, 1297,

# Residue Class 6n + 1 Prime: - Reference: http://oeis.org/A0024768

# 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613, 619

for i from 0 to 619 by 1 do

if type(i,residueclass6nplus1prime) then printf("%d, ",i); end if;

end do;

7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397, 409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601, 607, 613, 619,

# Residue Class 6n + 5 Prime: - Reference: http://oeis.org/A007528

# 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569

for i from 0 to 569 by 1 do

if type(i,residueclass6nplus5prime) then printf("%d, ",i); end if;

end do;

5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569,

# Residue Class 8n + 1 Prime: - Reference: http://oeis.org/A007519

# 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353, 401, 409, 433, 449, 457, 521, 569, 577, 593, 601, 617, 641, 673, 761, 769, 809, 857, 881, 929, 937, 953, 977, 1009, 1033, 1049, 1097, 1129, 1153, 1193, 1201, 1217, 1249, 1289, 1297, 1321, 1361

for i from 0 to 641 by 1 do

if type(i,residueclass8nplus1prime) then printf("%d, ",i); end if;

end do;

17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353, 401, 409, 433, 449, 457, 521, 569, 577, 593, 601, 617, 641,

# Residue Class 8n + 3 Prime: - Reference: http://oeis.org/A007520

# 3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 283, 307, 331, 347, 379, 419, 443, 467, 491, 499, 523, 547, 563, 571, 587, 619, 643, 659, 683, 691, 739, 787, 811, 827, 859, 883, 907, 947, 971, 1019, 1051, 1091, 1123, 1163, 1171, 1187

for i from 0 to 547 by 1 do

if type(i,residueclass8nplus3prime) then printf("%d, ",i); end if;

end do;

3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 283, 307, 331, 347, 379, 419, 443, 467, 491, 499, 523, 547,

# Residue Class 8n + 5 Prime: - Reference: http://oeis.org/A007521

# 5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269, 277, 293, 317, 349, 373, 389, 397, 421, 461, 509, 541, 557, 613, 653, 661, 677, 701, 709, 733, 757, 773, 797, 821, 829, 853, 877, 941, 997, 1013, 1021, 1061, 1069, 1093, 1109

for i from 0 to 557 by 1 do

if type(i,residueclass8nplus5prime) then printf("%d, ",i); end if;

end do;

5, 13, 29, 37, 53, 61, 101, 109, 149, 157, 173, 181, 197, 229, 269, 277, 293, 317, 349, 373, 389, 397, 421, 461, 509, 541, 557,

# Residue Class 8n + 7 Prime: - Reference: http://oeis.org/A007522

# 7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 887, 911, 919, 967, 983, 991, 1031, 1039, 1063, 1087, 1103, 1151

for i from 0 to 599 by 1 do

if type(i,residueclass8nplus7prime) then printf("%d, ",i); end if;

end do;

7, 23, 31, 47, 71, 79, 103, 127, 151, 167, 191, 199, 223, 239, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599,

# Residue Class 10n + 1 Prime: - http://oeis.org/A030430

# 11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631, 641, 661, 691, 701, 751, 761, 811, 821, 881, 911, 941, 971, 991, 1021, 1031, 1051, 1061, 1091, 1151, 1171, 1181, 1201, 1231, 1291

for i from 0 to 631 by 1 do

if type(i,residueclass10nplus1prime) then printf("%d, ",i); end if;

end do;

11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 331, 401, 421, 431, 461, 491, 521, 541, 571, 601, 631,

# Residue Class 10n + 3 Prime: - Reference: http://oeis.org/A030431

# 3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 353, 373, 383, 433, 443, 463, 503, 523, 563, 593, 613, 643, 653, 673, 683, 733, 743, 773, 823, 853, 863, 883, 953, 983, 1013, 1033, 1063, 1093, 1103, 1123, 1153, 1163, 1193

for i from 0 to 593 by 1 do

if type(i,residueclass10nplus3prime) then printf("%d, ",i); end if;

end do;

3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 353, 373, 383, 433, 443, 463, 503, 523, 563, 593,

# Residue Class 10n + 7 Prime: - Reference: http://oeis.org/A030432

# 7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577, 587, 607, 617, 647, 677, 727, 757, 787, 797, 827, 857, 877, 887, 907, 937, 947, 967, 977, 997, 1087, 1097, 1117, 1187, 1217, 1237

for i from 0 to 577 by 1 do

if type(i,residueclass10nplus7prime) then printf("%d, ",i); end if;

end do;

7, 17, 37, 47, 67, 97, 107, 127, 137, 157, 167, 197, 227, 257, 277, 307, 317, 337, 347, 367, 397, 457, 467, 487, 547, 557, 577,

# Residue Class 10n + 9 Prime: - Reference: http://oeis.org/A030433

# 19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359, 379, 389, 409, 419, 439, 449, 479, 499, 509, 569, 599, 619, 659, 709, 719, 739, 769, 809, 829, 839, 859, 919, 929, 1009, 1019, 1039, 1049, 1069, 1109, 1129, 1229, 1249, 1259, 1279, 1289

for i from 0 to 619 by 1 do

if type(i,residueclass10nplus9prime) then printf("%d, ",i); end if;

end do;

19, 29, 59, 79, 89, 109, 139, 149, 179, 199, 229, 239, 269, 349, 359, 379, 389, 409, 419, 439, 449, 479, 499, 509, 569, 599, 619,

# Safe Prime: - Reference: http://oeis.org/A005385

# 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903

for i from 0 to 479 by 1 do

if type(i,safeprime) then printf("%d, ",i); end if;

end do;

5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479,

# Sophie Germain Prime: - Reference: http://oeis.org/A005384

# 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559

for i from 0 to 641 by 1 do

if type(i,sophiegermainprime) then printf("%d, ",i); end if;

end do;

2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641,

# Star Prime: - Reference: http://oeis.org/A083577

# 13, 37, 73, 181, 337, 433, 541, 661, 937, 1093, 2053, 2281, 2521, 3037, 3313, 5581, 5953, 6337, 6733, 7561, 7993, 8893, 10333, 10837, 11353, 12421, 12973, 13537, 15913, 18481, 20533, 21961, 25741, 27337, 32413, 33301, 36037, 36973, 42841

for i from 0 to 1093 by 1 do

if type(i,starprime) then printf("%d, ",i); end if;

end do;

13, 37, 73, 181, 337, 433, 541, 661, 937, 1093,

# Thabit Prime: - Reference: http://oeis.org/A007505

# 2, 5, 11, 23, 47, 191, 383, 6143, 786431, 51539607551, 824633720831, 26388279066623, 108086391056891903, 55340232221128654847, 226673591177742970257407, 59421121885698253195157962751, 30423614405477505635920876929023

for i from 0 to 383 by 1 do

if type(i,thabitprime) then printf("%d, ",i); end if;

end do;

2, 5, 11, 23, 47, 191, 383,

# Wagstaff Form of (2p + 1) / 3 Prime: - Reference: http://oeis.org/A000979

# 3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, 62357403192785191176690552862561408838653121833643

for i from 0 to 2731 by 1 do

if type(i,wagstaffformprime) then printf("%d, ",i); end if;

end do;

3, 11, 43, 683, 2731,

# Wagstaff Value p Prime: - Reference: http://oeis.org/A000978

# 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701, 1709, 2617, 3539, 5807, 10501, 10691, 11279, 12391, 14479, 42737, 83339, 95369, 117239, 127031, 138937, 141079, 267017, 269987, 374321, 986191, 4031399

for i from 0 to 701 by 1 do

if type(i,wagstaffvalueprime) then printf("%d, ",i); end if;

end do;

3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167, 191, 199, 313, 347, 701,

# Wieferich base 2 prime: - Reference: http://oeis.org/A001220

# 1093, 3511

for i from 0 to 3511 by 1 do

if type(i,wieferichbase2prime) then printf("%d, ",i); end if;

end do;

1093, 3511,

# Wieferich base 3 prime: - Reference: http://oeis.org/A014127

# 11, 1006003

if type(11,wieferichbase3prime) then printf("%d, ",11); end if;

if type(1006003,wieferichbase3prime) then printf("%d, ",1006003); end if;

11, 1006003,

# Wieferich base 5 prime: - Reference: http://oeis.org/A123692

# 2, 20771, 40487, 53471161, 1645333507, 6692367337, 188748146801

for i from 0 to 40487 by 1 do

if type(i,wieferichbase5prime) then printf("%d, ",i); end if;

end do;

2, 20771, 40487,

# Wieferich base 6 prime: - Reference: http://en.wikipedia.org/wiki/List_of_prime_numbers

# 66161, 534851, 3152573

if type(66161,wieferichbase6prime) then printf("%d, ",66161); end if;

if type(534851,wieferichbase6prime) then printf("%d, ",534851); end if;

if type(3152573,wieferichbase6prime) then printf("%d, ",3152573); end if;

66161, 534851, 3152573,

# Wieferich base 7 prime: - Reference: http://oeis.org/A123693

# 5, 491531

if type(5,wieferichbase7prime) then printf("%d, ",5); end if;

if type(491531,wieferichbase7prime) then printf("%d, ",491531); end if;

5, 491531,

# Wieferich base 10 prime: - Reference: http://oeis.org/A045616

# 3, 487, 56598313

for i from 0 to 487 by 1 do

if type(i,wieferichbase10prime) then printf("%d, ",i); end if;

end do;

3, 487,

# Wieferich base 11 prime: - Reference: http://en.wikipedia.org/wiki/List_of_prime_numbers

# 71

for i from 0 to 71 by 1 do

if type(i,wieferichbase11prime) then printf("%d, ",i); end if;

end do;

71,

# Wieferich base 12 prime: - Reference: http://oeis.org/A111027

# 2693, 123653

if type(2693,wieferichbase12prime) then printf("%d, ",2693); end if;

if type(123653,wieferichbase12prime) then printf("%d, ",123653); end if;

2693, 123653,

# Wieferich base 13 prime: - Reference: http://oeis.org/A128667

# 2, 863, 1747591

for i from 0 to 863 by 1 do

if type(i,wieferichbase13prime) then printf("%d, ",i); end if;

end do;

2, 863,

# Wieferich base 17 prime: - Reference: http://en.wikipedia.org/wiki/List_of_prime_numbers

# 2, 3, 46021, 48947

for i from 0 to 48947 by 1 do

if type(i,wieferichbase17prime) then printf("%d, ",i); end if;

end do;

2, 3, 46021, 48947,

# Wieferich base 19 prime: - Reference: http://oeis.org/A090968

# 3, 7, 13, 43, 137, 63061489

for i from 0 to 137 by 1 do

if type(i,wieferichbase19prime) then printf("%d, ",i); end if;

end do;

3, 7, 13, 43, 137,

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# Michael Carter, Computer Scientist and Software Developer