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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 3

%I

%S 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,

%T 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,

%U 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

%N 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

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

%H Pierre CAMI, <a href="/A159700/b159700.txt">Table of n, a(n) for n=1..50000</a>

%e 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

%o (Haskell)

%o a159700 n = length $ filter (\(p, q) -> p < q - 2 && a164292 q == 1) $

%o zip ps (map (2 * n -) ps)

%o where ps = filter ((== 1) . a164292) [1..n]

%o -- _Reinhard Zumkeller_, Mar 13 2014

%Y Cf. A164292.

%K nonn,look

%O 1,8

%A _Pierre CAMI_, Apr 20 2009

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Last modified October 1 01:24 EDT 2022. Contains 357133 sequences. (Running on oeis4.)