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A159700
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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
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3
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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
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OFFSET
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1,8
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COMMENTS
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conjecture : for n>2104 there is at least one such pair of primes p+q=2*n
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LINKS
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EXAMPLE
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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
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PROG
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(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]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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