A023296 Primes that remain prime through 3 iterations of function f(x) = 9x + 2.

19, 103, 113, 151, 239, 283, 313, 599, 929, 1481, 2411, 2549, 2593, 2741, 2819, 2969, 3931, 4091, 4463, 4523, 5279, 5923, 6781, 7759, 8209, 8363, 9749, 10133, 10531, 12919, 14071, 15053, 15361, 16229, 16453, 16493, 16573, 16703, 17041, 17783, 18253

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 9*p+2, 81*p+20 and 729*p+182 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023233 and A023265.

Programs

Magma

[n: n in [1..450000] | IsPrime(n) and IsPrime(9*n+2) and IsPrime(81*n+20) and IsPrime(729*n+182)]; // Vincenzo Librandi, Aug 04 2010

Maple

A023296:=n->`if`(isprime(n) and isprime(9*n+2) and isprime(81*n+20) and isprime(729*n+182), n, NULL): seq(A023296(n), n=1..5*10^4); # Wesley Ivan Hurt, Feb 22 2017

Mathematica

Select[Prime@ Range@ 2100, Times @@ Boole@ PrimeQ@ NestList[9 # + 2 &, #, 3] > 0 &] (* Michael De Vlieger, Feb 22 2017 *)
Select[Prime[Range[2100]],AllTrue[Rest[NestList[9#+2&,#,3]],PrimeQ]&] (* Harvey P. Dale, May 14 2024 *)