A126148 Primes p such that pq+p+q is prime, where q is the next prime after p.

2, 3, 5, 11, 13, 17, 19, 23, 41, 43, 47, 59, 79, 83, 89, 101, 109, 113, 137, 163, 167, 173, 223, 229, 257, 311, 383, 389, 409, 419, 439, 443, 479, 521, 547, 557, 577, 593, 613, 643, 647, 683, 773, 797, 809, 811, 853, 953, 983, 1019, 1049, 1097, 1109, 1151, 1171

Offset: 1

Author

J. M. Bergot, Mar 07 2007

Keywords

• nonn
• easy

Examples

			Take p = 13 and q = 17: product is 221 and sum is 30; add them to get 251, a prime. So 13 is a member.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096342, A000040, A001043, A006094, A126199, A096342.

Programs

Maple

a:=proc(n) if isprime(ithprime(n)*ithprime(n+1) +ithprime(n) +ithprime(n+1)) then ithprime(n) fi end: seq(a(n), n=1..250); # Emeric Deutsch, Mar 08 2007

Mathematica

Prime@Select[Range[200], PrimeQ[Prime[ # ]Prime[ # + 1] + Prime[ # ] + Prime[ # + 1]] &] (* Ray Chandler, Mar 07 2007 *)

PARI

v=List();p=2;forprime(q=3,1e4, if(isprime(p*q+p+q), listput(v,p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 26 2012

Extensions

Extended by Ray Chandler, Emeric Deutsch and Robert G. Wilson v, Mar 07 2007