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 A239936 Least k > 0 such that p(k)+q(n) is prime, where p(n) is the number of partitions of n and q(n) is the number of strict partitions of n. 1
 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 4, 3, 1, 4, 3, 3, 10, 3, 4, 5, 2, 1, 1, 1, 6, 5, 5, 1, 6, 2, 4, 1, 12, 1, 15, 13, 1, 3, 5, 4, 4, 1, 5, 5, 1, 2, 1, 12, 49, 1, 1, 2, 6, 6, 3, 14, 3, 3, 3, 6, 6, 16, 13, 16, 11, 1, 1, 4, 5, 3, 12, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Conjecture of Zhi-Wei Sun: a(n) < n for n > 1. LINKS Sean A. Irvine, Table of n, a(n) for n = 0..9999 Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014-2016. See Conjecture 4.1(ii). EXAMPLE a(5)=2 since q(5)+p(2)=3+2=5 is prime but q(5)+p(1)=4 is composite. MATHEMATICA a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsP[k] + PartitionsQ[n]], Return[k]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 19 2019 *) CROSSREFS Cf. A000009, A000040, A000041, A239675, A239736. Sequence in context: A265575 A352177 A277367 * A239701 A303755 A321279 Adjacent sequences: A239933 A239934 A239935 * A239937 A239938 A239939 KEYWORD nonn AUTHOR Sean A. Irvine, Mar 29 2014 STATUS approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)