A023317 Primes that remain prime through 4 iterations of function f(x) = 6x + 5.

11, 13, 83, 151, 317, 373, 1721, 3529, 4153, 4243, 4637, 4783, 5209, 5849, 5923, 6661, 8431, 10903, 11329, 14519, 16183, 16979, 20149, 26669, 27509, 27827, 29873, 29947, 32987, 33637, 33937, 34919, 35099, 35543, 36277, 36691, 38069, 38461, 41651, 47407

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 6*p+5, 36*p+35, 216*p+215 and 1296*p+1295 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023221, A023257, A023288, and A059325.

Programs

Magma

[n: n in [1..1000000] | IsPrime(n) and IsPrime(6*n+5) and IsPrime(36*n+35) and IsPrime(216*n+215) and IsPrime(1296*n+1295)] // Vincenzo Librandi, Aug 04 2010

Mathematica

if4Q[n_]:=AllTrue[Rest[NestList[6#+5&,n,4]],PrimeQ]; Select[Prime[ Range[ 5000]],if4Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 10 2018 *)