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 A228429 Number of ways to write n =  x + y (x, y > 0) with p(39, x) + p(40, y) prime, where p(m, k) denotes the m-gonal number (m-2)*k*(k-1)/2 + k. 5
 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 3, 1, 1, 4, 2, 2, 4, 1, 3, 1, 2, 5, 5, 1, 2, 3, 4, 3, 11, 4, 4, 2, 3, 4, 9, 6, 3, 5, 6, 3, 5, 4, 3, 9, 6, 3, 4, 7, 5, 13, 8, 3, 5, 5, 6, 13, 9, 9, 6, 3, 4, 6, 7, 3, 5, 5, 8, 5, 11, 8, 11, 8, 5, 10, 9, 5, 13, 9, 10, 11, 4, 7, 14, 12, 6, 11, 9, 5, 9, 15, 5, 14, 11, 6, 7, 8, 13, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS By a conjecture in A228425, we should have a(n) > 0 for all n > 1. Conjecture: For each m = 3, 4, ..., any sufficiently large integer n can be written as x + y (x, y > 0) with p(m, x) + p(m+1, y) prime. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, On universal sums of polygonal numbers, preprint, arXiv:0905.0635. EXAMPLE a(9) = 1 since 9 = 5 + 4 with p(39, 5) + p(40, 4) = 607 prime. a(26) = 1 since 26 = 19 + 7 with p(39, 19) + p (40, 7) = 7151 prime. MATHEMATICA p[m_, x_]:=(m-2)x(x-1)/2+x a[n_]:=Sum[If[PrimeQ[p[39, x]+p[40, n-x]], 1, 0], {x, 1, n-1}] Table[a[n], {n, 1, 100}] CROSSREFS Cf. A000040, A228425, A228428, A228430, A228431. Sequence in context: A072038 A284315 A262928 * A108316 A322426 A145574 Adjacent sequences:  A228426 A228427 A228428 * A228430 A228431 A228432 KEYWORD nonn AUTHOR Zhi-Wei Sun, Nov 10 2013 STATUS approved

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)