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 A234347 a(n) = |{0 < k < n: 3^k + 3^{phi(n-k)/2} - 1 is prime}|, where phi(.) is Euler's totient function. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Conjecture: a(n) > 0 for all n > 3. See also the conjecture in A234337. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..3000 EXAMPLE 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. MATHEMATICA 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}] CROSSREFS Cf. A000010, A000040, A000244, A234309, A234310, A234337, A234344, A234346. Sequence in context: A079086 A017839 A242294 * A286245 A279849 A106826 Adjacent sequences:  A234344 A234345 A234346 * A234348 A234349 A234350 KEYWORD nonn AUTHOR Zhi-Wei Sun, Dec 24 2013 STATUS approved

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Last modified June 25 12:01 EDT 2019. Contains 324352 sequences. (Running on oeis4.)