A242936 Numbers n such that n*prime(n) + (n+1)*(prime(n+1)) is semiprime.

2, 5, 9, 11, 13, 16, 17, 22, 23, 27, 28, 30, 31, 33, 37, 38, 41, 42, 44, 45, 47, 53, 56, 58, 61, 64, 65, 67, 68, 70, 73, 74, 75, 76, 80, 81, 84, 85, 88, 90, 92, 93, 96, 99, 102, 105, 106, 107, 108, 109, 110, 112, 114, 116, 117, 119, 122, 123, 124, 125, 126, 129

Offset: 1

Author

K. D. Bajpai, May 27 2014

Keywords

• nonn

Examples

			a(2) = 5: 5*prime(5) + (5+1)*prime(5+1) = 133 = 7 * 19 which is semiprime.
a(3) = 9: 9*prime(9) + (9+1)*prime(9+1) = 497 = 7 * 71 which is semiprime.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001358, A105455.

Programs

Maple

with(numtheory): A242936:= proc() if bigomega(n*ithprime(n) + (n+1)*ithprime(n+1) = 2 then return (n) : fi; end:  seq(A242936 (), n=1..500);

Mathematica

c = 0; Do[If[PrimeOmega[n*Prime[n] + (n+1)*Prime[n+1]]==2, c++; Print[c,"  ",n]], {n,1,35000}];