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A236831
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Number of ordered ways to write n = p + q with q > 0 such that p, p + 2 and p + prime(q) + 1 are all prime.
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6
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0, 0, 0, 0, 1, 0, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 1, 3, 1, 4, 3, 2, 3, 2, 3, 2, 3, 1, 2, 2, 4, 3, 1, 3, 3, 3, 3, 3, 4, 2, 4, 4, 4, 3, 2, 2, 3, 4, 3, 4, 4, 2, 3, 4, 5, 3, 2, 6, 5, 1, 4, 2, 5, 4, 4, 4, 1, 6, 4, 2, 5, 3, 4, 5, 1, 2, 3, 4, 4, 3, 5, 4, 7, 3, 3, 2, 3, 4, 5, 4
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OFFSET
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1,9
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COMMENTS
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Conjecture: a(n) > 0 for all n > 13.
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LINKS
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EXAMPLE
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a(12) = 1 since 12 = 5 + 7 with 5, 5 + 2 = 7 and 5 + prime(7) + 1 = 5 + 17 + 1 = 23 all prime.
a(85) = 1 since 85 = 29 + 56 with 29, 29 + 2 = 31 and 29 + prime(56) + 1 = 29 + 263 + 1 = 293 all prime.
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MATHEMATICA
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p[n_, m_]:=PrimeQ[m+2]&&PrimeQ[m+Prime[n-m]+1]
a[n_]:=Sum[If[p[n, Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}]
Table[a[n], {n, 1, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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