A023348 Primes that remain prime through 5 iterations of function f(x) = 8x + 3.

774791, 924731, 4593221, 5181641, 9905521, 11523361, 11755831, 12253321, 14078711, 14545331, 14928791, 18523361, 18686531, 24169001, 25614361, 26221051, 26834461, 30970201, 33446521, 40051021, 42888191, 43703201, 47528561, 48653951

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 8*p+3, 64*p+27, 512*p+219, 4096*p+1755 and 32768*p+14043 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

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

Crossrefs

Subsequence of A005124, A023229, A023261, A023292, and A023320.

Programs

Magma

[n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+3) and IsPrime(64*n+27) and IsPrime(512*n+219) and IsPrime(4096*n+1755) and IsPrime(32768*n+14043)] // Vincenzo Librandi, Aug 05 2010

Mathematica

n5Q[n_]:=And@@PrimeQ/@NestList[8#+3&,n,5]; Select[Prime[Range[ 3000000]], n5Q] (* Harvey P. Dale, Sep 03 2013 *)

Formula

a(n) == 31 (mod 70). - John Cerkan, Nov 04 2016