A023304 Primes that remain prime through 4 iterations of function f(x) = 2x + 5.

13, 31, 181, 541, 661, 1087, 1861, 2179, 2719, 3727, 7459, 8089, 8707, 9109, 10639, 17341, 19333, 22501, 23293, 29287, 32797, 39847, 40387, 42703, 46591, 51613, 53101, 56149, 56809, 57829, 59233, 80779, 87643, 89113, 89413, 91291, 93979, 94261, 98899

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 2*p+5, 4*p+15, 8*p+35 and 16*p+75 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, A023274, and A089038.

Programs

Magma

[n: n in [1..1000000] | IsPrime(n) and IsPrime(2*n+5) and IsPrime(4*n+15) and IsPrime(8*n+35) and IsPrime(16*n+75)]; // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime@ Range[10^4], Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 5 &, #, 4] > 0 &] (* Michael De Vlieger, Sep 27 2016 *)
Select[Prime[Range[10000]],AllTrue[Rest[NestList[2#+5&,#,4]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 23 2020 *)

Formula

a(n) == 1 (mod 6). - John Cerkan, Sep 27 2016

Extensions

Definition clarified by Harvey P. Dale, Oct 23 2020