OFFSET
2,6
COMMENTS
Conjecture of Zhi-Wei Sun: a(n) < n for n > 1.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 2..9999
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