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A239736
Least k > 0 such that p(n)+p(k)-1 is prime, where p(n) is the number of partitions of n.
3
1, 1, 1, 1, 1, 3, 2, 2, 2, 10, 3, 1, 3, 8, 3, 6, 4, 2, 4, 9, 9, 4, 4, 8, 2, 2, 2, 3, 11, 8, 4, 13, 19, 4, 1, 6, 3, 4, 2, 4, 26, 12, 5, 11, 11, 9, 6, 5, 25, 4, 24, 6, 4, 2, 5, 9, 9, 2, 7, 4, 28, 13, 8, 27, 9, 23, 3, 7, 2, 24, 36, 38, 9, 26, 16, 1
OFFSET
2,6
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, 2014. See Conjecture 4.1(ii).
EXAMPLE
a(7)=3, since p(7)+p(1)-1=15 and p(7)+p(2)-1=16 are composite, but p(7)+p(3)-1=17 is prime.
MATHEMATICA
a[n_] := For[k = 1, True, k++, If[PrimeQ[PartitionsP[n] + PartitionsP[k] - 1], Return[k]]];
Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Dec 12 2018 *)
PROG
(PARI) s=[]; for(n=2, 100, k=1; while(!isprime(numbpart(n)+numbpart(k)-1), k++); s=concat(s, k)); s \\ Colin Barker, Mar 26 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Sean A. Irvine, Mar 25 2014
STATUS
approved