A152091 Primes which are the sum of cousin prime pairs + 1.

11, 19, 31, 43, 79, 139, 163, 199, 211, 223, 331, 463, 619, 631, 883, 919, 1231, 1291, 1483, 1543, 1723, 1759, 1879, 2179, 2851, 2971, 3163, 3331, 3391, 3571, 3739, 4003, 4483, 4591, 4759, 4783, 4951, 5323, 5419, 5503, 6043, 6079, 6163, 6379, 6691, 7351

Offset: 2

Author

Cino Hilliard, Nov 24 2008

Keywords

• nonn

Comments

3 and 7 are the only cousin primes with another prime (5) between them. - Harvey P. Dale, Jul 28 2012

Examples

			prime(2)=3, 3 + 4 = 7, 3 + 7 + 1 = 11, the first term in the sequence.
		

Links

• John Cerkan, Table of n, a(n) for n = 2..10000

Programs

Mathematica

Join[{11},Select[Total/@Select[Partition[Prime[Range[600]],2,1], Last[#]-First[#]==4&]+1,PrimeQ]] (* Harvey P. Dale, Jul 28 2012 *)

PARI

g4(n) = for(x=2,n,p=prime(x);if(isprime(p+4),y=p+p+4+1;if(isprime(y), print1(y","))))

PARI

isA152091(n) = if(n%2==0,0,isprime(n) && isprime((n-5)/2) && isprime((n+3)/2)) \\ Michael B. Porter, Mar 17 2010

Formula

Cousin primes are prime pairs that differ by 4.