

A278210


Last residue class to appear in the partition numbers mod n.


2



0, 0, 0, 0, 4, 0, 6, 4, 8, 9, 10, 4, 6, 6, 4, 12, 0, 8, 10, 8, 6, 10, 18, 16, 21, 13, 16, 27, 24, 19, 27, 8, 10, 26, 29, 18, 25, 16, 0, 28, 27, 6, 32, 21, 19, 33, 13, 13, 13, 21, 0, 18, 23, 48, 28, 16, 26, 34, 26, 4, 33, 35, 4, 40, 52, 10, 65, 34, 62, 16, 40, 12, 66, 48, 21, 18, 6, 13, 72, 46, 19, 20
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OFFSET

1,5


COMMENTS

Let k be the smallest number such that {p(1), p(2), ..., p(k)} contains each residue class mod n, where p(m) is the mth partition number A000041(m). Then a(n) = p(k) mod n.


LINKS

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


FORMULA

a(n) = A000041(A278209(n)) mod n.


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) = 0.


MATHEMATICA

Table[k = 1; While[Length@ Union@ Map[Mod[PartitionsP@ #, n] &, Range@ k] != n, k++]; Mod[PartitionsP@ k, n], {n, 82}] (* Michael De Vlieger, Nov 21 2016 *)


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(t))))


CROSSREFS

Cf. A000041, A278209.
Sequence in context: A279433 A096272 A021715 * A291540 A075443 A021250
Adjacent sequences: A278207 A278208 A278209 * A278211 A278212 A278213


KEYWORD

nonn


AUTHOR

Charles R Greathouse IV, Nov 15 2016


STATUS

approved



