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

1,4

Links

Table of n, a(n) for n=1..80.

Example

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

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 *)

Crossrefs

Cf. A103960, A224748, A210481.

Sequence in context: A262446 A205147 A319447 * A358023 A056812 A210721

Adjacent sequences: A224958 A224959 A224960 * A224962 A224963 A224964

Keyword

nonn

Author

Jayanta Basu, Apr 21 2013

Status

approved