

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 mth partition number A000041(m).


2



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
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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



