A242937 Numbers n such that n*prime(n) + (n+1)*(prime(n+1)) + (n+2)*(prime(n+2)) is semiprime.

2, 4, 7, 8, 9, 11, 14, 16, 18, 19, 26, 32, 36, 38, 42, 44, 48, 50, 53, 71, 74, 78, 79, 82, 86, 94, 95, 98, 104, 108, 111, 114, 118, 122, 124, 126, 136, 141, 146, 154, 162, 166, 172, 174, 178, 180, 184, 186, 189, 190, 197, 200, 203, 206, 216, 219, 221, 223, 224

Offset: 1

Author

K. D. Bajpai, May 27 2014

Keywords

• nonn

Examples

			a(2) = 4: 4*prime(4) + (4+1)*prime(4+1) + (4+2)*prime(4+2) = 161 = 7 * 23 is semiprime.
a(5) = 9: 9*prime(9) + (9+1)*prime(9+1) + (9+2)*prime(9+2) = 838 = 2 * 419 is semiprime.
		

Links

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

Crossrefs

Cf. A000040, A001358, A105455.

Programs

Maple

with(numtheory):A242937:= proc() if bigomega(ithprime(n)*n + ithprime(n+1)*(n+1) + ithprime(n+2)*(n+2)) = 2 then return (n) : fi; end:  seq(A242937 (), n=1..500);

Mathematica

c = 0; Do[If[PrimeOmega[n*Prime[n] + (n+1)*Prime[n+1] + (n+2)*Prime[n+2]]==2, c++; Print[c,"  ",n]], {n,1,85000}];