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 1-7 of 7 results.

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 *)

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 *)

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 *)

A023301 Primes that remain prime through 3 iterations of function f(x) = 10x + 9.

Original entry on oeis.org

13, 139, 293, 331, 547, 967, 1049, 1399, 1567, 1889, 1997, 2087, 2137, 2309, 2423, 2437, 2753, 2939, 3719, 3761, 3919, 4451, 4517, 4621, 6089, 7001, 7741, 8423, 8849, 9437, 10487, 11657, 12007, 12347, 12823, 13469, 15289, 15373, 15661, 17737, 17989
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 10*p+9, 100*p+99 and 1000*p+999 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023240, A023270, and A102700.

Programs

  • Magma
    [n: n in [1..450000] | IsPrime(n) and IsPrime(10*n+9) and IsPrime(100*n+99) and IsPrime(1000*n+999)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    nrp3Q[n_]:=AllTrue[Rest[NestList[10#+9&,n,3]],PrimeQ]; Select[Prime[ Range[ 2100]],nrp3Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2019 *)

A023329 Primes that remain prime through 4 iterations of function f(x) = 10x + 9.

Original entry on oeis.org

13, 139, 293, 1889, 2939, 3719, 6089, 7741, 12823, 19753, 21391, 22861, 28513, 36721, 37967, 40949, 60899, 76519, 83621, 101747, 121687, 127549, 128239, 142099, 149197, 153817, 155581, 158489, 160159, 169283, 173651, 180749, 185831, 192037, 198221
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 10*p+9, 100*p+99, 1000*p+999 and 10000*p+9999 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023240, A023270, A023301, and A102700.

Programs

  • Magma
    [n: n in [1..5000000] | IsPrime(n) and IsPrime(10*n+9) and IsPrime(100*n+99) and IsPrime(1000*n+999) and IsPrime(10000*n+9999)]; // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Prime[Range[20000]],AllTrue[Rest[NestList[10#+9&,#,4]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 16 2020 *)

Formula

a(n) == 9 or 13 (mod 14). - John Cerkan, Oct 09 2016

Extensions

Definition clarified by Harvey P. Dale, Feb 16 2020
Showing 1-7 of 7 results.

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