A224965 Let p = prime(n). a(n) = number of primes q less than p, such that both p*q+p+q and p*q-p-q are primes.

0, 0, 2, 3, 1, 2, 2, 2, 1, 2, 1, 1, 3, 2, 1, 1, 1, 3, 2, 2, 1, 3, 1, 0, 4, 0, 1, 2, 5, 0, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 4, 2, 1, 0, 2, 5, 1, 1, 3, 1, 3, 3, 3, 0, 1, 2, 4, 1, 4, 4, 2, 2, 2, 6, 2, 5, 2, 3, 3, 2, 4, 5, 3, 2, 1, 3, 1, 3, 3, 3, 2, 2, 3, 2

Offset: 1

Author

Jayanta Basu, Apr 21 2013

Keywords

• nonn

Examples

			For n=3, p=5, there are a(3)=2 solutions 2,3 since 5*2+5+2=17, 5*2-5-2=3 and 5*3+5+3=23, 5*3-5-3=7. Also for n=5, p=11, there is a(5)=1 solution in the form of 11*3+11+3=47, 11*3-11-3=19.
		

Crossrefs

Cf. A224748, A224908, A224925, A224962.

Programs

Mathematica

Table[p = Prime[n]; c = 0; i = 1; While[i < n, q1 = p*Prime[i]; q2 = p + Prime[i]; If[PrimeQ[q1 + q2] && PrimeQ[q1 - q2], c = c + 1]; i++]; c, {n, 85}]