A023274 Primes that remain prime through 3 iterations of function f(x) = 2x + 5.

13, 31, 37, 67, 73, 181, 367, 541, 661, 997, 1087, 1117, 1327, 1861, 2179, 2293, 2473, 2713, 2719, 3271, 3727, 4363, 5281, 5443, 5749, 7459, 8089, 8707, 9109, 9181, 9337, 10357, 10639, 12553, 13183, 14923, 16183, 16249, 17341, 17419, 17761, 17923, 17989

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 2*p+5, 4*p+15 and 8*p+35 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023205, A023243, and of A089038.

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15) and IsPrime(8*n+35)] // Vincenzo Librandi, Aug 04 2010

Maple

select(t -> isprime(t) and isprime(2*t+5) and isprime(4*t+15) and isprime(8*t+35), [seq(t,t=7..20000,6)]);# Robert Israel, Sep 18 2016

Mathematica

Select[Prime@ Range@ 2100, Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 5 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 16 2016 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 16 2016