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

%I A126148 #20 Oct 31 2019 11:39:29
%S A126148 2,3,5,11,13,17,19,23,41,43,47,59,79,83,89,101,109,113,137,163,167,
%T A126148 173,223,229,257,311,383,389,409,419,439,443,479,521,547,557,577,593,
%U A126148 613,643,647,683,773,797,809,811,853,953,983,1019,1049,1097,1109,1151,1171
%N A126148 Primes p such that pq+p+q is prime, where q is the next prime after p.
%H A126148 Charles R Greathouse IV, <a href="/A126148/b126148.txt">Table of n, a(n) for n = 1..10000</a>
%e A126148 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.
%p A126148 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
%t A126148 Prime@Select[Range[200], PrimeQ[Prime[ # ]Prime[ # + 1] + Prime[ # ] + Prime[ # + 1]] &] (* _Ray Chandler_, Mar 07 2007 *)
%o A126148 (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
%Y A126148 Cf. A096342, A000040, A001043, A006094, A126199, A096342.
%K A126148 nonn,easy
%O A126148 1,1
%A A126148 _J. M. Bergot_, Mar 07 2007
%E A126148 Extended by _Ray Chandler_, _Emeric Deutsch_ and _Robert G. Wilson v_, Mar 07 2007