A278209 a(n) is the smallest number k such that {p(1), p(2), ..., p(k)} contains each residue class mod n, where p(m) is the m-th partition number A000041(m).

1, 2, 3, 11, 30, 9, 73, 26, 56, 32, 202, 55, 41, 86, 45, 55, 54, 58, 43, 70, 107, 224, 92, 98, 110, 173, 73, 115, 102, 73, 140, 128, 335, 97, 132, 129, 109, 128, 129, 113, 133, 207, 253, 301, 310, 239, 180, 244, 122, 152, 178, 245, 249, 351, 536, 262, 252, 314, 202, 310

Offset

1,2

Comments

It has been conjectured that for each r and n, there is some k such that p(k) = r mod n; on that conjecture, this sequence is defined for all n.

If congruence classes of p(m) were chosen uniformly at random, the expected value of this sequence would be ~ n log n.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Charles R Greathouse IV, C+Arb code for computing this sequence

Example

p(1) = 1, p(2) = 2, p(3) = 3, p(4) = 5, p(5) = 7, p(6) = 11, p(7) = 15, p(8) = 22, p(9) = 30, p(10) = 42, and p(11) = 56. Mod 4 these are 1, 2, 3, 1, 3, 3, 3, 2, 2, 2, and 0 respectively. The last term to appear is 0 mod 4 at index 11, so a(4) = 11.

Prog

(PARI) a(n)=if(n==1, return(1)); my(v=vectorsmall(n), s=1, t, k=1); v[2]=1; while(s<n, t=numbpart(k++)%n; if(v[t+1]==0, v[t+1]=1; if(s++==n, return(k))))
(C) See Greathouse link.

Crossrefs

Cf. A000041, A278210.

Sequence in context: A267902 A003455 A103275 * A195732 A038987 A142957

Adjacent sequences: A278206 A278207 A278208 * A278210 A278211 A278212

Keyword

nonn

Author

Charles R Greathouse IV, Nov 15 2016

Status

approved