A023307 Primes that remain prime through 4 iterations of function f(x) = 3x + 2.

1129, 10009, 11489, 12539, 13859, 30029, 63079, 77359, 99119, 121039, 124669, 169409, 194749, 205589, 246329, 330329, 349519, 351829, 354839, 361279, 369539, 384589, 395719, 399769, 416989, 429109, 446819, 527599, 532489, 544259, 575119

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 3*p+2, 9*p+8, 27*p+26, and 81*p+80 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023208, A023246, A023277, and A024893.

Programs

Magma

[n: n in [1..1000000] | IsPrime(n) and IsPrime(3*n+2) and IsPrime(9*n+8) and IsPrime(27*n+26) and IsPrime(81*n+80)] // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[50000]],AllTrue[Rest[NestList[3#+2&,#,4]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 13 2015 *)

Formula

a(n) == 9 or 69 (mod 70). - John Cerkan, Oct 04 2016