A023329 Primes that remain prime through 4 iterations of function f(x) = 10x + 9.

13, 139, 293, 1889, 2939, 3719, 6089, 7741, 12823, 19753, 21391, 22861, 28513, 36721, 37967, 40949, 60899, 76519, 83621, 101747, 121687, 127549, 128239, 142099, 149197, 153817, 155581, 158489, 160159, 169283, 173651, 180749, 185831, 192037, 198221

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 10*p+9, 100*p+99, 1000*p+999 and 10000*p+9999 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023240, A023270, A023301, and A102700.

Programs

Magma

[n: n in [1..5000000] | IsPrime(n) and IsPrime(10*n+9) and IsPrime(100*n+99) and IsPrime(1000*n+999) and IsPrime(10000*n+9999)]; // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[20000]],AllTrue[Rest[NestList[10#+9&,#,4]],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 16 2020 *)

Formula

a(n) == 9 or 13 (mod 14). - John Cerkan, Oct 09 2016

Extensions

Definition clarified by Harvey P. Dale, Feb 16 2020