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A240545
Least k > 0 such that n + p(k) is prime, where p(k) is the number of partitions of k.
2
2, 1, 1, 2, 1, 2, 1, 8, 3, 2, 1, 2, 1, 9, 3, 2, 1, 2, 1, 8, 3, 2, 1, 9, 4, 8, 3, 2, 1, 2, 1, 8, 4, 11, 3, 2, 1, 8, 3, 2, 1, 2, 1, 9, 3, 2, 1, 10, 4, 8, 3, 2, 1, 9, 4, 10, 3, 2, 1, 2, 1, 8, 4, 15, 3, 2, 1, 8, 3, 2, 1, 2, 1, 9, 4, 8, 3, 2, 1, 8, 3, 2
OFFSET
0,1
COMMENTS
Conjecture of Zhi-Wei Sun: a(n) < n for n > 7.
Verified up to 6*10^8. - Sean A. Irvine, Apr 07 2014
LINKS
Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014. See Conjecture 4.1(ii).
EXAMPLE
a(7)=8 because k=8 is the smallest k such that 7+A000041(k) is prime.
MATHEMATICA
a[n_] := For[k = 1, True, k++, If[PrimeQ[n + PartitionsP[k]], Return[k]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 15 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Sean A. Irvine, Apr 07 2014
STATUS
approved