A224961 a(n) = number of primes of the form p * q + 2 where p is the prime(n) and q is any prime < p.

0, 0, 1, 2, 1, 2, 2, 3, 3, 2, 1, 4, 0, 4, 4, 4, 5, 4, 4, 3, 2, 4, 4, 3, 5, 3, 4, 4, 6, 4, 7, 4, 4, 7, 5, 5, 6, 5, 6, 8, 5, 7, 7, 6, 3, 9, 5, 8, 5, 8, 7, 10, 9, 7, 8, 8, 5, 8, 8, 9, 8, 8, 10, 7, 11, 13, 8, 10, 10, 10, 11, 9, 12, 9, 13, 11, 9, 12, 7, 11

Offset: 1

Author

Jayanta Basu, Apr 21 2013

Keywords

• nonn

Examples

			For n=4, p=7, there are a(4)=2 solutions from 7*3+2=23 and 7*5+2=37.
		

Crossrefs

Cf. A103960, A224748, A210481.

Programs

Mathematica

Table[p = Prime[n]; c = 0; i = 1; While[i < n, If[PrimeQ[p*Prime[i] + 2], c = c + 1]; i++]; c, {n, 80}]
Table[Count[Prime[n]Prime[Range[n-1]]+2,?PrimeQ],{n,80}] (* _Harvey P. Dale, Feb 28 2023 *)