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

1,1

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Subsequence of A023240, A023270, A023301, and A102700.

Sequence in context: A088096 A271069 A023301 * A280745 A142896 A193700

Adjacent sequences: A023326 A023327 A023328 * A023330 A023331 A023332

Keyword

nonn

Author

David W. Wilson

Extensions

Definition clarified by Harvey P. Dale, Feb 16 2020

Status

approved