A023251 Primes that remain prime through 2 iterations of function f(x) = 4x + 9.

7, 41, 43, 47, 67, 71, 97, 103, 137, 263, 293, 307, 397, 421, 467, 491, 571, 587, 593, 683, 727, 757, 883, 907, 1021, 1061, 1063, 1097, 1153, 1373, 1427, 1433, 1453, 1523, 1567, 1657, 1747, 1811, 1867, 2141, 2251, 2281, 2287, 2647, 2693, 2791, 2797, 2857, 2927

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 4*p+9 and 16*p+45 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A111199.

Programs

Magma

[n: n in [0..100000] | IsPrime(n) and IsPrime(4*n+9) and IsPrime(16*n+45)]; // Vincenzo Librandi, Aug 04 2010

Mathematica

rpQ[n_]:=AllTrue[Rest[NestList[4#+9&,n,2]],PrimeQ]; Select[Prime[ Range[ 500]],rpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 03 2019 *)