A023351 Primes that remain prime through 5 iterations of function f(x) = 8x + 9.

294793, 2586943, 5360623, 6351613, 7965743, 11141083, 11378453, 13458923, 14884823, 15585523, 18691633, 25387763, 29964293, 30766283, 32388253, 38647723, 40653433, 48716873, 48786593, 52628473, 54270533, 55507853, 56575633, 59103403

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 8*p+9, 64*p+81, 512*p+657, 4096*p+5265 and 32768*p+42129 are also primes. - Vincenzo Librandi, Aug 05 2010

Links

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

Crossrefs

Subsequence of A023232, A023264, A023295, A023323, and of A153762.

Programs

Magma

[n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+9) and IsPrime(64*n+81) and IsPrime(512*n+657) and IsPrime(4096*n+5265) and IsPrime(32768*n+42129)] // Vincenzo Librandi, Aug 05 2010

Mathematica

prp5Q[n_]:=AllTrue[Rest[NestList[8#+9&,n,5]],PrimeQ]; Select[Prime[Range[3513000]],prp5Q] (* Harvey P. Dale, May 25 2024 *)
prp5Q2[n_] := AllTrue[NestList[8 # + 9 &, n, 5], PrimeQ]; Select[Range[23, 59120000, 70], prp5Q2] (* Faster  than the first Mathematica program above. *) (* Harvey P. Dale, May 25 2024 *)

Formula

a(n) == 23 (mod 70). - John Cerkan, Nov 13 2016