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 1-4 of 4 results.

A023249 Primes that remain prime through 2 iterations of function f(x) = 3x + 10.

Original entry on oeis.org

3, 7, 11, 17, 19, 47, 67, 109, 149, 151, 199, 227, 233, 347, 353, 359, 397, 431, 457, 487, 563, 571, 577, 607, 709, 809, 919, 947, 997, 1013, 1033, 1069, 1103, 1117, 1151, 1187, 1279, 1361, 1367, 1451, 1601, 1607, 1697, 1699, 1801, 1811, 1823, 1831, 1871, 1913
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 3*p+10 and 9*p+40 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023211.

Programs

  • Magma
    [n: n in [0..100000] | IsPrime(n) and IsPrime(3*n+10) and IsPrime(9*n+40)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Range@ 2000, Times @@ Boole@ PrimeQ@ NestList[3 # + 10 &, #, 2] > 0 &] (* Michael De Vlieger, Sep 13 2016 *)

A023310 Primes that remain prime through 4 iterations of function f(x) = 3x + 10.

Original entry on oeis.org

3, 199, 233, 709, 1361, 1367, 2137, 2879, 5519, 5987, 7283, 9719, 11699, 14983, 16417, 17881, 20939, 24481, 30467, 31663, 31741, 35107, 35863, 46811, 47869, 49261, 58207, 60497, 63317, 64781, 68777, 73453, 74021, 79901, 85487, 85571, 94327, 94999
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 3*p+10, 9*p+40, 27*p+130 and 81*p+400 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

Crossrefs

Subsequence of A023211, A023249, and A023280.

Programs

  • Magma
    [n: n in [1..1000000] | IsPrime(n) and IsPrime(3*n+10) and IsPrime(9*n+40) and IsPrime(27*n+130) and IsPrime(81*n+400)] // Vincenzo Librandi, Aug 04 2010
  • Mathematica
    Select[Range[10^5], Times @@ Boole@ PrimeQ@ NestList[3 # + 10 &, #, 4] > 0 &] (* Michael De Vlieger, Oct 04 2016 *)
  • PARI
    is(n)=isprime(n) && isprime(3*n+10) && isprime(9*n+40) && isprime(27*n+130) && isprime(81*n+400) \\ Charles R Greathouse IV, Oct 04 2016

Formula

a(n) == 3 or 9 (mod 14). - John Cerkan, Oct 04 2016

A023338 Primes that remain prime through 5 iterations of function f(x) = 3x + 10.

Original entry on oeis.org

233, 709, 11699, 16417, 24481, 31663, 63317, 94999, 172279, 185243, 205081, 228713, 240347, 266681, 285539, 334511, 372059, 395719, 479327, 583501, 734197, 786613, 856627, 863711, 1146091, 1187167, 1188259, 1423067, 1534591, 1562269, 1594301
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Primes p such that 3*p+10, 9*p+40, 27*p+130, 81*p+400 and 243*p+1210 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

Crossrefs

Subsequence of A023211, A023249, A023280, and A023310.

Programs

  • Magma
    [n: n in [1..25000000] | IsPrime(n) and IsPrime(3*n+10) and IsPrime(9*n+40) and IsPrime(27*n+130) and IsPrime(81*n+400) and IsPrime(243*n+1210)] // Vincenzo Librandi, Aug 05 2010
  • Mathematica
    rp5Q[p_]:=AllTrue[Rest[NestList[3#+10&,p,5]],PrimeQ]; Select[Prime[ Range[ 150000]],rp5Q] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 17 2020 *)
  • PARI
    is(n)=isprime(n) && isprime(3*n+10) && isprime(9*n+40) && isprime(27*n+130) && isprime(81*n+400) && isprime(243*n+1210) \\ Charles R Greathouse IV, Oct 11 2016

Formula

a(n) == 9 (mod 14). - John Cerkan, Oct 11 2016

Extensions

Definition clarified by Harvey P. Dale, Mar 17 2020

A274505 Primes p such that 3*p-10 and 3*p+10 are prime numbers.

Original entry on oeis.org

7, 11, 17, 19, 23, 31, 47, 61, 67, 89, 101, 107, 109, 137, 151, 163, 199, 283, 347, 353, 373, 397, 401, 409, 431, 439, 457, 479, 487, 523, 577, 607, 619, 641, 647, 661, 691, 761, 787, 809, 907, 929, 1033, 1087, 1103, 1153, 1201, 1229, 1307, 1319
Offset: 1

Views

Author

Vincenzo Librandi, Jun 30 2016

Keywords

Comments

Intersection of A023211 and A230227.

Examples

			7 is a term because 3*7-10 = 11 and 3*7+10 = 31 are primes.

Links

Crossrefs

Cf. A023211, A164568, A230227.

Programs

  • Magma
    [p: p in PrimesUpTo(1500) |IsPrime(3*p-10) and IsPrime(3*p+10)];
  • Mathematica
    Select[Prime[Range[400]], PrimeQ[3 # - 10] && PrimeQ[3 # + 10] &]
Showing 1-4 of 4 results.

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