A023322 Primes that remain prime through 4 iterations of function f(x) = 8x + 7.

7949, 25589, 55799, 61379, 69959, 70229, 74609, 174569, 188369, 204719, 220469, 225629, 233759, 250919, 286619, 363659, 552749, 592139, 658349, 735419, 783269, 827549, 931949, 1018889, 1065839, 1126319, 1132739, 1187939, 1215629, 1378529

Offset

1,1

Comments

Primes p such that 8*p+7, 64*p+63, 512*p+511 and 4096*p+4095 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

John Cerkan, Table of n, a(n) for n = 1..10000

Formula

a(n) == 9 (mod 10). - John Cerkan, Oct 08 2016

Mathematica

rp4Q[p_]:=AllTrue[Rest[NestList[8#+7&, p, 4]], PrimeQ]; Select[Prime[Range[110000]], rp4Q] (* Harvey P. Dale, Aug 03 2023 *)

Prog

(Magma) [n: n in [1..5000000] | IsPrime(n) and IsPrime(8*n+7) and IsPrime(64*n+63) and IsPrime(512*n+511) and IsPrime(4096*n+4095)] // Vincenzo Librandi, Aug 04 2010

Crossrefs

Subsequence of A023231, A023263, A023294, and A139487.

Sequence in context: A302901 A179708 A162010 * A064246 A260959 A316906

Adjacent sequences: A023319 A023320 A023321 * A023323 A023324 A023325

Keyword

nonn

Author

David W. Wilson

Status

approved