A023273 Primes that remain prime through 3 iterations of function f(x) = 2x + 3.

2, 5, 47, 67, 97, 137, 197, 277, 307, 607, 617, 1307, 1427, 2857, 5717, 6047, 6217, 6257, 6997, 9377, 9787, 9967, 11197, 12097, 13297, 13997, 14347, 16057, 18757, 18947, 20887, 21517, 21587, 21757, 24197, 26227, 28097, 28447, 32117, 33767, 34367, 35117

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 2*p+3, 4*p+9 and 8*p+21 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[p: p in PrimesUpTo(50000) | IsPrime(2*p+3) and IsPrime(4*p+9) and IsPrime(8*p+21)]; // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime[Range[5000]],AllTrue[Rest[NestList[2#+3&,#,3]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 01 2016 *)

PARI

isok(n)=isprime(n) && isprime(2*n+3) && isprime(4*n+9) && isprime(8*n+21) \\ Edward Jiang, Sep 09 2014

Python

from sympy import prime, isprime
A023273_list = [p for p in (prime(n) for n in range(1,10**2)) if isprime(2*p+3) and isprime(4*p+9) and isprime(8*p+21)] # Chai Wah Wu, Sep 09 2014