A242243 Semiprimes sp of the form p^2 + q + 1 where p and q are consecutive primes.

15, 33, 187, 309, 559, 1411, 1897, 2263, 2869, 3543, 6979, 10717, 11559, 11995, 22353, 32953, 39009, 54529, 57363, 58333, 66313, 77011, 80383, 113917, 120759, 124969, 147079, 158011, 167701, 175983, 177673, 237661, 241581, 253519, 299767, 310813, 376387, 381309

Offset: 1

Author

K. D. Bajpai, May 09 2014

Keywords

• nonn

Examples

			a(1) = 15 = 3^2 + 5 + 1 = 3 * 5 is semiprime, 3 and 5 are consecutive primes.
a(2) = 33 = 5^2 + 7 + 1 = 3 * 11 is semiprime, 5 and 7 are consecutive primes.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5970

Crossrefs

Cf. A000040, A001358, A045636, A145292, A228183.

Programs

Maple

with(numtheory): A242243:= proc()local k ; k:=(ithprime(x)^2+ithprime(x+1)+1);if  bigomega(k)=2 then RETURN (k); fi;end: seq(A242243 (),x=1..500);

Mathematica

Select[Table[Prime[n]^2 + Prime[n + 1] + 1, {n, 500}], PrimeOmega[#] == 2 &]