A023301 Primes that remain prime through 3 iterations of function f(x) = 10x + 9.

13, 139, 293, 331, 547, 967, 1049, 1399, 1567, 1889, 1997, 2087, 2137, 2309, 2423, 2437, 2753, 2939, 3719, 3761, 3919, 4451, 4517, 4621, 6089, 7001, 7741, 8423, 8849, 9437, 10487, 11657, 12007, 12347, 12823, 13469, 15289, 15373, 15661, 17737, 17989

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 10*p+9, 100*p+99 and 1000*p+999 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, and A102700.

Programs

Magma

[n: n in [1..450000] | IsPrime(n) and IsPrime(10*n+9) and IsPrime(100*n+99) and IsPrime(1000*n+999)] // Vincenzo Librandi, Aug 04 2010

Mathematica

nrp3Q[n_]:=AllTrue[Rest[NestList[10#+9&,n,3]],PrimeQ]; Select[Prime[ Range[ 2100]],nrp3Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2019 *)