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 A236470 a(n) = |{0 < k < n: p = prime(k) + phi(n-k), p + 2 and prime(p) + 2 are all prime}}, where phi(.) is Euler's totient function. 6
 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 2, 1, 2, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 0, 1, 1, 0, 3, 0, 1, 0, 1, 3, 0, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,14 COMMENTS Conjecture: a(n) > 0 for all n > 948. We have verified this for n up to 50000. The conjecture implies that there are infinitely many primes p with p + 2 and prime(p) + 2 both prime. See A236458 for such primes p. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 EXAMPLE a(12) = 1 since prime(5) + phi(7) = 11 + 6 = 17, 17 + 2 = 19 and prime(17) + 2 = 59 + 2 = 61 are all prime. a(97) = 1 since prime(7) + phi(90) = 17 + 24 = 41, 41 + 2 = 43 and prime(41) + 2 = 179 + 2 = 181 are all prime. MATHEMATICA p[n_]:=PrimeQ[n]&&PrimeQ[n+2]&&PrimeQ[Prime[n]+2] f[n_, k_]:=Prime[k]+EulerPhi[n-k] a[n_]:=Sum[If[p[f[n, k]], 1, 0], {k, 1, n-1}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000010, A000040, A001359, A006512, A236097, A236456, A236458, A236468. Sequence in context: A218854 A172303 A064391 * A206589 A086011 A124760 Adjacent sequences:  A236467 A236468 A236469 * A236471 A236472 A236473 KEYWORD nonn AUTHOR Zhi-Wei Sun, Jan 26 2014 STATUS approved

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Last modified July 29 04:52 EDT 2021. Contains 346340 sequences. (Running on oeis4.)