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A219966
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Number of ways to write n=p+q+(n mod 2)q with q<=n/2 and p, q, q+6 all prime
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 3, 2, 2, 3, 2, 3, 3, 2, 1, 4, 3, 1, 4, 3, 1, 4, 2, 3, 3, 2, 2, 4, 3, 2, 4, 2, 2, 5, 3, 4, 5, 2, 1, 5, 3, 2, 4, 1, 1, 5, 4, 4, 4, 3, 2, 5, 3, 2, 4, 3, 4, 5, 3, 4, 6, 3, 3, 6, 3, 3, 8, 5, 2, 6, 3, 4, 6, 2, 2, 9, 5, 3, 5, 4, 2, 6, 4
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OFFSET
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1,17
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COMMENTS
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Conjecture: a(n)>0 for all n>11.
This conjecture is stronger than Goldbach's conjecture and Lemoine's conjecture. It can be further strengthened; see A219055 and the comments there.
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LINKS
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EXAMPLE
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a(19)=1 since 19=5+2*7 with 5, 7, 7+6 all prime.
a(20)=1 since 20=13+7 with 13, 7, 7+6 all prime.
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MATHEMATICA
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a[n_]:=a[n]=Sum[If[PrimeQ[Prime[k]+6]==True&&PrimeQ[n-(1+Mod[n, 2])Prime[k]]==True, 1, 0], {k, 1, PrimePi[n/2]}]
Do[Print[n, " ", a[n]], {n, 1, 10000}]
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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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