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A234347
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a(n) = |{0 < k < n: 3^k + 3^{phi(n-k)/2} - 1 is prime}|, where phi(.) is Euler's totient function.
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14
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0, 0, 0, 1, 2, 3, 4, 3, 3, 5, 3, 5, 6, 7, 2, 6, 7, 11, 7, 3, 6, 8, 7, 4, 11, 8, 8, 6, 6, 10, 7, 6, 8, 5, 6, 4, 8, 4, 6, 6, 6, 11, 10, 3, 9, 6, 6, 4, 10, 6, 7, 3, 4, 9, 8, 9, 7, 9, 5, 9, 7, 9, 8, 4, 6, 9, 10, 7, 8, 9, 10, 5, 6, 12, 5, 6, 9, 10, 8, 9, 7, 8, 8, 10
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OFFSET
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1,5
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COMMENTS
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Conjecture: a(n) > 0 for all n > 3.
See also the conjecture in A234337.
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LINKS
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EXAMPLE
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a(4) = 1 since 3^1 + 3^{phi(3)/2} - 1 = 5 is prime.
a(5) = 2 since 3^1 + 3^{phi(4)/2} - 1 = 5 and 3^2 + 3^{phi(3)/2} - 1 are both prime.
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MATHEMATICA
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f[n_, k_]:=3^k+3^(EulerPhi[n-k]/2)-1
a[n_]:=Sum[If[PrimeQ[f[n, k]], 1, 0], {k, 1, 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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