A023275 Primes that remain prime through 3 iterations of function f(x) = 2x + 7.

5, 23, 293, 593, 953, 2063, 3323, 4133, 4583, 8243, 8783, 9173, 9203, 14723, 15383, 16103, 16763, 18413, 19163, 20123, 25733, 29453, 37223, 38783, 39443, 40253, 41903, 42923, 44753, 45863, 49433, 51473, 54443, 54623, 54713, 57383, 58913, 63353, 66533

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Primes p such that 2*p+7, 4*p+21 and 8*p+49 are also primes. - Vincenzo Librandi, Aug 04 2010

Links

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

Crossrefs

Subsequence of A023206, A023244, and of A105760.

Programs

Magma

[n: n in [1..100000] | IsPrime(n) and IsPrime(2*n+7) and IsPrime(4*n+21) and IsPrime(8*n+49)] // Vincenzo Librandi, Aug 04 2010

Mathematica

Select[Prime@ Range@ 7000, Times @@ Boole@ PrimeQ@ Rest@ NestList[2 # + 7 &, #, 3] > 0 &] (* Michael De Vlieger, Sep 19 2016 *)
Select[Prime[Range[7000]],AllTrue[Rest[NestList[2#+7&,#,3]],PrimeQ]&] (* Harvey P. Dale, Dec 26 2022 *)

PARI

is(n)=isprime(n) && isprime(2*n+7) && isprime(4*n+21) && isprime(8*n+49) \\ Charles R Greathouse IV, Sep 20 2016

Formula

a(n) == 23 (mod 30) for n > 1. - John Cerkan, Sep 16 2016