A023278 Primes that remain prime through 3 iterations of function f(x) = 3x + 4.

23, 683, 1663, 2753, 3203, 6073, 6323, 7523, 8243, 9293, 9613, 15173, 19913, 21023, 21683, 25183, 26633, 29663, 34613, 34703, 39293, 41953, 43283, 45533, 52813, 59393, 62473, 65053, 66763, 71713, 71993, 81533, 81953, 84523, 87833, 103843, 104183

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 3*p+4, 9*p+16 and 27*p+52 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023209, A023247, and of A034936.

Programs

Magma

[n: n in [1..150000] | IsPrime(n) and IsPrime(3*n+4) and IsPrime(9*n+16) and IsPrime(27*n+52)] // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime@ Range[10^4], Times @@ Boole@ PrimeQ@ Rest@ NestList[3 # + 4 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 19 2016 *)

PARI

is(n)=isprime(n) && isprime(3*n+4) && isprime(9*n+16) && isprime(27*n+52) \\ Charles R Greathouse IV, Sep 20 2016

Formula

a(n) == 3 (mod 10). - John Cerkan, Sep 16 2016