A159700 Number of different pairs of primes p,q such that : p<(q-2), p is a twin prime of p-2 or p+2 and q is a twin prime of q-2 or q+2, 2*n=p+q

0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 3, 4, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 4, 3, 3, 4, 2, 1, 2, 1, 2, 4, 2, 0, 0, 0, 2, 4, 3, 2, 2, 2, 4, 6, 3, 2, 4, 2, 1, 2, 1, 2, 4, 2, 1, 2, 2, 3, 4, 2, 2, 4, 3, 3, 4, 2, 2, 4, 2, 3, 6, 3, 1, 2, 1, 3, 6, 4, 2, 2, 1, 2, 4, 3, 4, 6, 4, 3, 4, 2, 6, 12

Offset

1,8

Comments

conjecture : for n>2104 there is at least one such pair of primes p+q=2*n

Links

Pierre CAMI, Table of n, a(n) for n=1..50000

Example

3+13=16,5+11=16 so for n=8 2 pairs p,q such that p+q=2*8, p<(q-2) p and q have a twin prime

Prog

(Haskell)
a159700 n = length $ filter (\(p, q) -> p < q - 2 && a164292 q == 1) $
                            zip ps (map (2 * n -) ps)
                     where ps = filter ((== 1) . a164292) [1..n]
-- Reinhard Zumkeller, Mar 13 2014

Crossrefs

Cf. A164292.

Sequence in context: A237348 A373360 A037813 * A083534 A174664 A027386

Adjacent sequences: A159697 A159698 A159699 * A159701 A159702 A159703

Keyword

nonn,look

Author

Pierre CAMI, Apr 20 2009

Status

approved