A210481 Given n-th prime p, a(n) = number of primes of the form p * q - 2 where q is any prime < p.

0, 0, 1, 1, 2, 2, 1, 1, 4, 2, 2, 4, 3, 2, 4, 3, 4, 3, 4, 4, 6, 3, 4, 5, 3, 5, 5, 4, 3, 6, 4, 7, 5, 4, 6, 5, 7, 9, 7, 5, 6, 5, 6, 6, 8, 5, 7, 9, 5, 6, 7, 5, 7, 7, 9, 10, 3, 11, 8, 11, 6, 9, 8, 12, 8, 9, 7, 10, 9, 7, 8, 8, 6, 14, 8, 10, 11, 11, 12, 11, 7, 7

Offset: 1

Author

Jayanta Basu, Apr 18 2013

Keywords

• nonn

Comments

Very similar to A103960. - T. D. Noe, Apr 18 2013

a(A137291(n)) = A103960(A137291(n)) - 1. - Reinhard Zumkeller, Jul 30 2015

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A103960, A224748.

Cf. A010051, A000040, A103960, A137291.

Programs

Haskell

a210481 n = sum [a010051' $ p * q - 2 |
                 let p = a000040 n, q <- takeWhile (< p) a000040_list]
-- Reinhard Zumkeller, Jul 30 2015

Mathematica

Table[p = Prime[n]; c = 0; Do[If[PrimeQ[p*Prime[i] - 2], c = c + 1], {i, n - 1}]; c, {n, 82}]
Table[With[{pr=Prime[Range[n]]},Count[Most[pr]Last[pr]-2,?PrimeQ]],{n,90}] (* _Harvey P. Dale, Jul 19 2020 *)