A167915 Primes which are the sums of two consecutive nonprimes (A141468).

5, 17, 19, 29, 31, 41, 43, 53, 67, 71, 79, 89, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 151, 163, 173, 181, 191, 197, 199, 211, 223, 229, 233, 239, 241, 251, 257, 269, 271, 281, 283, 293, 307, 311, 317, 331, 337, 349, 353, 367, 373, 379, 389, 401, 409

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 15 2009

Keywords

• nonn

Comments

Five together with primes that are the sum of two consecutive composite numbers.

Examples

			a(1)=1+4=5, a(2)=8+9=17.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A060254, A141468, A176902.

Programs

Magma

[2*n+1: n in [1..300] | (not IsPrime(n) eq not IsPrime(n+1)) and IsPrime(2*n+1)]; // G. C. Greubel, Nov 10 2023

Mathematica

2*Select[Range[300], !PrimeQ[#] == !PrimeQ[#+1] && PrimeQ[2*#+1] &] + 1 (* G. C. Greubel, Jul 01 2016; Nov 10 2023 *)

SageMath

[2*n+1 for n in (1..300) if  (not is_prime(n)) - (not is_prime(n+1)) == 0 and is_prime(2*n+1)] # G. C. Greubel, Nov 10 2023

Formula

a(n+1) = A060254(n) = A176902(n+1). - Juri-Stepan Gerasimov, Apr 28 2010

Extensions

Typo corrected and terms checked by D. S. McNeil, Nov 17 2010