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 A237715 Number of ordered ways to write n = p + q (q > 0) with p, prime(p) - p + 1 and prime(prime(q)) - prime(q) + 1 all prime. 2
 0, 0, 1, 2, 2, 3, 2, 3, 4, 2, 3, 2, 2, 4, 2, 5, 2, 3, 3, 4, 3, 2, 3, 3, 4, 5, 4, 2, 3, 4, 4, 4, 2, 4, 2, 4, 5, 2, 2, 3, 4, 4, 4, 5, 5, 3, 6, 2, 6, 5, 4, 4, 4, 4, 5, 2, 3, 2, 4, 4, 5, 3, 6, 5, 9, 5, 6, 4, 4, 7, 6, 5, 7, 3, 8, 5, 7, 4, 5, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Conjecture: a(n) > 0 for all n > 2, and a(n) = 1 only for n = 3. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014. EXAMPLE a(3) = 1 since 3 = 2 + 1 with 2, prime(2) - 2 + 1 = 3 - 1 = 2 and prime(prime(1)) - prime(1) + 1 = prime(2) - 2 + 1  = 2 all prime. a(7) = 2 since 7 = 3 + 4 with 3, prime(3) - 3 + 1 = 5 - 2 = 3 and prime(prime(4)) - prime(4) + 1 = prime(7) - 7 + 1 = 17 - 6 = 11 are all prime, and 7 = 5 + 2 with 5, prime(5) - 5 + 1 = 11 - 4 = 7 and prime(prime(2)) - prime(2) + 1 = prime(3) - 3 + 1 = 5 - 2 = 3 all prime. MATHEMATICA pq[k_]:=PrimeQ[Prime[Prime[k]]-Prime[k]+1] a[n_]:=Sum[If[pq[k]&&pq[n-Prime[k]], 1, 0], {k, 1, PrimePi[n-1]}] Table[a[n], {n, 1, 80}] CROSSREFS Cf. A000040, A234694, A234695, A238766, A238776, A238814. Sequence in context: A101037 A002199 A218829 * A238458 A182744 A308355 Adjacent sequences:  A237712 A237713 A237714 * A237716 A237717 A237718 KEYWORD nonn AUTHOR Zhi-Wei Sun, Mar 06 2014 STATUS approved

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Last modified April 9 14:25 EDT 2020. Contains 333355 sequences. (Running on oeis4.)