A023310 Primes that remain prime through 4 iterations of function f(x) = 3x + 10.

3, 199, 233, 709, 1361, 1367, 2137, 2879, 5519, 5987, 7283, 9719, 11699, 14983, 16417, 17881, 20939, 24481, 30467, 31663, 31741, 35107, 35863, 46811, 47869, 49261, 58207, 60497, 63317, 64781, 68777, 73453, 74021, 79901, 85487, 85571, 94327, 94999

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 3*p+10, 9*p+40, 27*p+130 and 81*p+400 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023211, A023249, and A023280.

Programs

Magma

[n: n in [1..1000000] | IsPrime(n) and IsPrime(3*n+10) and IsPrime(9*n+40) and IsPrime(27*n+130) and IsPrime(81*n+400)] // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Range[10^5], Times @@ Boole@ PrimeQ@ NestList[3 # + 10 &, #, 4] > 0 &] (* Michael De Vlieger, Oct 04 2016 *)

PARI

is(n)=isprime(n) && isprime(3*n+10) && isprime(9*n+40) && isprime(27*n+130) && isprime(81*n+400) \\ Charles R Greathouse IV, Oct 04 2016

Formula

a(n) == 3 or 9 (mod 14). - John Cerkan, Oct 04 2016