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A235714 Consider N = numerator( 1/p! + 1/q! ) where p = prime(n), q = prime(n+1) for n = 1,2,3,.... Append N to sequence if it is a prime.

%I A235714 #10 Jan 18 2014 13:30:21
%S A235714 2,7,43,157,7,72775847,139,523,751,193,19183,22651,140165120353,1051,
%T A235714 37057,433,7459,8263,19248899859613286187907,1564207235629,10453,877,
%U A235714 1993,45183625504351,121453,89248200525047,1505879629
%N A235714 Consider N = numerator( 1/p! + 1/q! ) where p = prime(n), q = prime(n+1) for n = 1,2,3,.... Append N to sequence if it is a prime.
%H A235714 K. D. Bajpai, <a href="/A235714/b235714.txt">Table of n, a(n) for n = 1..1300</a>
%e A235714 43 is in the sequence because ( 1/5! + 1/7! ) = (1/120 + 1/5040) = 43/5040: numerator(43/5040) = 43 which is prime.
%p A235714 KD := proc() local a,b,d,e; a:=ithprime(n)!; b:= ithprime(n+1)!; d:=(1/a) + (1/b); e:=numer(d); if isprime(e) then RETURN (e); fi;end: seq(KD(), n=1..100);
%t A235714 k={}; Do[p=Prime[n];q=Prime[n+1];  p2=Numerator[1/p!+1/q!]; If[PrimeQ[p2],AppendTo[k,p2]],{n,150}]; k
%Y A235714 Cf. A000040, A120833.
%K A235714 nonn
%O A235714 1,1
%A A235714 _K. D. Bajpai_, Jan 15 2014