A159700 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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) $