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A237839
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a(n) = |{0 < k <= n: q = |{p <= k*n: p and p + 2 are both prime}| and q + 2 are both prime}|.
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3
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0, 0, 0, 2, 1, 3, 2, 3, 1, 2, 2, 3, 3, 2, 2, 5, 2, 3, 3, 4, 2, 2, 2, 3, 1, 2, 2, 3, 3, 2, 3, 2, 2, 3, 6, 7, 5, 5, 3, 4, 3, 3, 4, 3, 3, 4, 4, 4, 5, 4, 5, 3, 3, 4, 3, 2, 2, 3, 4, 3, 4, 3, 3, 6, 6, 5, 5, 4, 5, 3, 5, 8, 4, 3, 3, 4, 1, 3, 4, 3
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OFFSET
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1,4
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COMMENTS
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Conjecture: a(n) > 0 for all n > 3, and a(n) = 1 only for n = 5, 9, 25, 77, 104.
See also A237838 for a similar conjecture involving Sophie Germain primes.
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LINKS
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EXAMPLE
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a(9) = 1 since {p <= 4*9: p and p + 2 are both prime} = {3, 5, 11, 17, 29} has cardinality 5 and {5, 7} is a twin prime pair.
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MATHEMATICA
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TQ[n_]:=PrimeQ[n]&&PrimeQ[n+2]
tq[n_]:=Sum[If[PrimeQ[Prime[k]+2], 1, 0], {k, 1, PrimePi[n]}]
a[n_]:=Sum[If[TQ[tq[k*n]], 1, 0], {k, 1, n}]
Table[a[n], {n, 1, 80}]
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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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