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 A237127 Number of ways to write n = k + m (0 < k < m) with k and m terms of A072281. 8
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 3, 2, 3, 2, 3, 3, 3, 2, 2, 4, 3, 3, 2, 2, 4, 3, 4, 3, 4, 4, 3, 3, 4, 5, 4, 1, 3, 3, 5, 4, 4, 4, 4, 5, 3, 4, 2, 4, 4, 4, 5, 2, 4, 1, 4, 4, 4, 4, 1, 3, 4, 4, 5, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,15 COMMENTS Conjecture: a(n) > 0 for all n > 11. Clearly, this implies the twin prime conjecture. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(13) = 1 since 13 = 5 + 8 with phi(5) - 1 = 3, phi(5) + 1 = 5, phi(8) - 1 = 3 and phi(8) + 1 = 5 all prime. a(60) = 1 since 60 = 18 + 42 with phi(18) - 1 = 5, phi(18) + 1 = 7, phi(42) - 1 = 11 and phi(42) + 1 = 13 all prime. a(84) = 1 since 84 = 7 + 77 with phi(7) - 1 = 5, phi(7) + 1 = 7, phi(77) - 1 = 59 and phi(77) + 1 = 61 all prime. MATHEMATICA PQ[n_]:=PrimeQ[EulerPhi[n]-1]&&PrimeQ[EulerPhi[n]+1] a[n_]:=Sum[If[PQ[k]&&PQ[n-k], 1, 0], {k, 1, (n-1)/2}] Table[a[n], {n, 1, 70}] CROSSREFS Cf. A000010, A000040, A001359, A006512, A014574, A072281. Sequence in context: A305030 A110917 A070956 * A262746 A007828 A070804 Adjacent sequences:  A237124 A237125 A237126 * A237128 A237129 A237130 KEYWORD nonn AUTHOR Zhi-Wei Sun, Feb 04 2014 STATUS approved

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Last modified October 23 12:00 EDT 2018. Contains 316527 sequences. (Running on oeis4.)