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.

2, 7, 43, 157, 7, 72775847, 139, 523, 751, 193, 19183, 22651, 140165120353, 1051, 37057, 433, 7459, 8263, 19248899859613286187907, 1564207235629, 10453, 877, 1993, 45183625504351, 121453, 89248200525047, 1505879629

Offset: 1

Author

K. D. Bajpai, Jan 15 2014

Keywords

• nonn

Examples

			43 is in the sequence because ( 1/5! + 1/7! ) = (1/120 + 1/5040) = 43/5040: numerator(43/5040) = 43 which is prime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1300

Crossrefs

Cf. A000040, A120833.

Programs

Maple

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);

Mathematica

k={}; Do[p=Prime[n];q=Prime[n+1];  p2=Numerator[1/p!+1/q!]; If[PrimeQ[p2],AppendTo[k,p2]],{n,150}]; k