cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 14 results. Next

A157974 Primes p such that 12*p + 11 is also prime.

Original entry on oeis.org

3, 5, 13, 19, 29, 31, 41, 53, 59, 61, 71, 73, 101, 109, 113, 131, 151, 173, 199, 211, 223, 239, 241, 251, 263, 283, 293, 313, 389, 409, 419, 439, 449, 491, 503, 521, 523, 571, 593, 631, 641, 643, 659, 673, 701, 733, 769, 809, 811, 823, 839, 853, 883, 929, 953
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 10 2009

Keywords

Links

Crossrefs

Cf. A136082, A136083, A023213, A023221, A023235, A023240.

Programs

  • Magma
    [n: n in [0..1000] | IsPrime(n) and IsPrime(12*n + 11)]; // Vincenzo Librandi, Feb 03 2014
  • Mathematica
    q=11;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[1000]], PrimeQ[12 # + 11]&] (* Vincenzo Librandi, Feb 03 2014 *)

A023257 Primes that remain prime through 2 iterations of function f(x) = 6x + 5.

Original entry on oeis.org

2, 11, 13, 17, 31, 37, 41, 43, 71, 73, 79, 83, 97, 137, 139, 151, 163, 181, 191, 193, 197, 269, 277, 307, 317, 347, 373, 409, 431, 503, 577, 743, 811, 823, 911, 919, 941, 967, 983, 1021, 1033, 1049, 1051, 1093, 1163, 1187, 1201, 1361, 1373, 1423, 1493, 1571, 1597
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 6*p+5 and 36*p+35 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023221.

Programs

  • Magma
    [n: n in [1..100000] | IsPrime(n) and IsPrime(6*n+5) and IsPrime(36*n+35)] // Vincenzo Librandi, Aug 04 2010

A157975 Primes p such that 16*p + 15 is also prime.

Original entry on oeis.org

2, 7, 11, 13, 23, 29, 37, 53, 61, 67, 71, 79, 89, 97, 103, 109, 113, 131, 137, 139, 149, 167, 179, 197, 211, 223, 257, 277, 293, 313, 317, 337, 379, 383, 397, 419, 431, 439, 443, 467, 571, 601, 617, 631, 641, 643, 653, 659, 677, 691, 719, 733, 739, 743, 809
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 10 2009

Keywords

Links

Crossrefs

Cf. A136082, A136083, A023213, A023221, A023235, A023240, A157974, A136083, A136084, A089440, A136085

Programs

  • Magma
    [n: n in [0..1000] | IsPrime(n) and IsPrime(16*n + 15)]; // Vincenzo Librandi, Feb 03 2014
  • Mathematica
    q=15;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[1000]], PrimeQ[16 # + 15]&] (* Vincenzo Librandi, Feb 03 2014 *)

A157978 Primes p such that 4*p - 3 is also a prime.

Original entry on oeis.org

2, 5, 11, 19, 23, 29, 59, 61, 71, 79, 89, 101, 103, 109, 113, 131, 149, 151, 191, 193, 233, 239, 263, 283, 313, 331, 353, 359, 373, 389, 401, 431, 439, 479, 499, 521, 523, 541, 569, 571, 599, 619, 631, 653, 659, 673, 683, 701, 709, 739, 743, 751, 761, 773, 829
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 10 2009

Keywords

Links

Crossrefs

Cf. A136082, A136083, A023213, A023221, A023235, A023240, A157974, A136083, A136084, A136085, A136086, A136087, A089440, A157975, A157976, A157977.

Programs

  • Magma
    [n: n in [0..2000] | IsPrime(n) and IsPrime(4*n - 3)]; // Vincenzo Librandi, Feb 03 2014
  • Mathematica
    q=3;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p-q],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[1000]],PrimeQ[4 # - 3]&] (* Vincenzo Librandi, Feb 03 2014 *)

A023288 Primes that remain prime through 3 iterations of function f(x) = 6x + 5.

Original entry on oeis.org

2, 11, 13, 31, 71, 83, 151, 163, 193, 197, 317, 347, 373, 503, 577, 811, 911, 919, 1049, 1051, 1201, 1423, 1721, 1907, 2089, 2243, 2543, 2719, 2963, 3529, 3583, 3607, 3797, 4091, 4153, 4217, 4243, 4409, 4591, 4637, 4783, 5209, 5557, 5783, 5849, 5923, 6091
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 6*p+5, 36*p+35 and 216*p+215 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023221, A023257, and A059325.

Programs

  • Magma
    [n: n in [1..150000] | IsPrime(n) and IsPrime(6*n+5) and IsPrime(36*n+35) and IsPrime(216*n+215)] // Vincenzo Librandi, Aug 04 2010

A157976 Primes p such that 18*p + 17 is also prime.

Original entry on oeis.org

2, 3, 5, 13, 19, 23, 37, 47, 53, 67, 79, 83, 89, 103, 109, 149, 157, 167, 193, 229, 233, 257, 263, 277, 313, 347, 349, 383, 389, 419, 439, 457, 467, 487, 499, 523, 563, 569, 593, 599, 619, 677, 719, 727, 769, 773, 823, 829, 857, 863, 877, 937, 1013, 1039, 1049
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 10 2009

Keywords

Links

Crossrefs

Cf. A136082, A136083, A023213, A023221, A023235, A023240, A157974, A136083, A136084, A136085, A136086, A136087, A089440, A157975.

Programs

  • Magma
    [n: n in [0..1100] | IsPrime(n) and IsPrime(18*n + 17)]; // Vincenzo Librandi, Feb 03 2014
  • Mathematica
    q=17;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[1000]], PrimeQ[18 # + 17]&] (* Vincenzo Librandi, Feb 03 2014 *)

A157977 Primes p such that 20*p + 19 is also prime.

Original entry on oeis.org

2, 3, 11, 17, 23, 29, 41, 71, 101, 149, 167, 233, 239, 251, 263, 269, 281, 293, 317, 347, 353, 401, 449, 461, 491, 503, 557, 563, 569, 647, 683, 743, 797, 857, 941, 947, 953, 977, 1019, 1031, 1091, 1103, 1151, 1163, 1193, 1217, 1283, 1289, 1319, 1361, 1373
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 10 2009

Keywords

Links

Crossrefs

Cf. A136082, A136083, A023213, A023221, A023235, A023240, A157974, A136083, A136084, A136085, A136086, A136087, A089440, A157975, A157976.

Programs

  • Magma
    [n: n in [0..2000] | IsPrime(n) and IsPrime(20*n + 19)]; // Vincenzo Librandi, Feb 03 2014
  • Mathematica
    q=19;lst={};Do[p=Prime[n];If[PrimeQ[(q+1)*p+q],AppendTo[lst,p]],{n,6!}];lst
Select[Prime[Range[250]],PrimeQ[20#+19]&] (* Harvey P. Dale, Jul 04 2011 *)

A023317 Primes that remain prime through 4 iterations of function f(x) = 6x + 5.

Original entry on oeis.org

11, 13, 83, 151, 317, 373, 1721, 3529, 4153, 4243, 4637, 4783, 5209, 5849, 5923, 6661, 8431, 10903, 11329, 14519, 16183, 16979, 20149, 26669, 27509, 27827, 29873, 29947, 32987, 33637, 33937, 34919, 35099, 35543, 36277, 36691, 38069, 38461, 41651, 47407
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 6*p+5, 36*p+35, 216*p+215 and 1296*p+1295 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023221, A023257, A023288, and A059325.

Programs

  • Magma
    [n: n in [1..1000000] | IsPrime(n) and IsPrime(6*n+5) and IsPrime(36*n+35) and IsPrime(216*n+215) and IsPrime(1296*n+1295)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    if4Q[n_]:=AllTrue[Rest[NestList[6#+5&,n,4]],PrimeQ]; Select[Prime[ Range[ 5000]],if4Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 10 2018 *)

A023345 Primes that remain prime through 5 iterations of function f(x) = 6x + 5.

Original entry on oeis.org

13, 4637, 5849, 5923, 16183, 16979, 34919, 36277, 67003, 79337, 115571, 159739, 175141, 245753, 249133, 305717, 341569, 359353, 383833, 437263, 455317, 498497, 511519, 567121, 579961, 581699, 633797, 683831, 693431, 849197, 972197, 1022449
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 6*p+5, 36*p+35, 216*p+215, 1296*p+1295 and 7776*p+7775 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023221, A023257, A023288, A023317, and A059325.

Programs

  • Magma
    [n: n in [1..10000000] | IsPrime(n) and IsPrime(6*n+5) and IsPrime(36*n+35) and IsPrime(216*n+215) and IsPrime(1296*n+1295) and IsPrime(7776*n+7775)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    Select[Range[1100000],And@@PrimeQ[NestList[6#+5&,#,5]]&] (* Harvey P. Dale, Mar 31 2012 *)

A106079 Primes p such that 5*p + 6 and 6*p + 5 are primes.

Original entry on oeis.org

7, 11, 13, 29, 37, 41, 79, 83, 97, 107, 113, 137, 139, 151, 163, 181, 193, 197, 239, 263, 347, 373, 389, 401, 421, 431, 443, 449, 487, 503, 541, 557, 643, 653, 701, 821, 839, 883, 911, 1033, 1051, 1093, 1129, 1163, 1201, 1217, 1259, 1283, 1303, 1373
Offset: 1

Views

Author

Zak Seidov, May 07 2005

Keywords

Links

Crossrefs

Intersection of A023219 and A023221. - Michel Marcus, Nov 06 2018

Programs

  • Magma
    [p: p in PrimesUpTo(5000)|IsPrime(5*p+6) and IsPrime(6*p+5)] // Vincenzo Librandi, Jan 30 2011
  • Maple
    select(n -> isprime(n) and isprime(5*n+6) and isprime(6*n+5), [seq(2*i+1,i=1..1000)]); # Robert Israel, Aug 04 2014
  • Mathematica
    Select[Prime[Range[220]], PrimeQ[6#+5]&&PrimeQ[5#+6]&]
  • PARI
    forprime(p=1,10^4,if(isprime(5*p+6)&&isprime(6*p+5),print1(p,", "))) \\ Derek Orr, Aug 04 2014
Showing 1-10 of 14 results. Next

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