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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
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
Sequence in context: A265575 A352177 A277367 * A239701 A303755 A321279
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.)