A023293 Primes that remain prime through 3 iterations of function f(x) = 8x + 5.

43, 103, 199, 1039, 1303, 2311, 2857, 3673, 4513, 4663, 5743, 5953, 8431, 9721, 12391, 14143, 14533, 17599, 18457, 19507, 21211, 23719, 24169, 25621, 28663, 29023, 31963, 33409, 35311, 36979, 37423, 40867, 40939, 43891, 44371, 44983, 45841, 46747, 46807

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 8*p+5, 64*p+45 and 512*p+365 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023230, A023262, and A105133.

Programs

Magma

[n: n in [1..450000] | IsPrime(n) and IsPrime(8*n+5) and IsPrime(64*n+45) and IsPrime(512*n+365)]; // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[5000]],AllTrue[Rest[NestList[8#+5&,#,3]],PrimeQ]&] (* Harvey P. Dale, Sep 19 2022 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 23 2016