A103960 Number of primes p such that prime(n)*p - 2 is prime and p <= prime(n).

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

Offset: 1

Author

Lei Zhou, Feb 22 2005

Keywords

• easy
• nonn

Comments

Conjecture: All items of this sequence are greater than or equal to 1. Tested to prime(1000000).

a(A137291(n)) = A210481(A137291(n)) + 1. - Reinhard Zumkeller, Jul 30 2015

Examples

			Prime(1)*2-2 = 2, so a(1)=1;
Prime(3) = 5, 5*3-2 = 13, 5*5-2 = 23, so a(3)=2;
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A103959.

Cf. A010051, A000040, A137291, A210481.

Programs

Haskell

a103960 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]; ct=0; Do[pk=Prime[k]; If[PrimeQ[p*pk-2], ct=ct+1], {k, n}]; ct, {n, 100}]