A067694 Minimum number of distinct parts in a self-conjugate partition of n, or 0 if n=2.

0, 1, 0, 2, 1, 2, 3, 2, 2, 1, 3, 2, 2, 2, 3, 2, 1, 2, 3, 2, 2, 2, 3, 2, 2, 1, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 1, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 1, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 1, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 1, 2, 3

Offset

0,4

Comments

There are no self-conjugate partitions of 2, so we set a(2)=0.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Formula

a(0)=a(2)=0; a(n^2)=1; a(4n+2)=3 for n>0; a(n)=2 in all other cases.

Mathematica

a[0]=a[2]=0; a[n_] := Which[IntegerQ[Sqrt[n]], 1, Mod[n, 4]==2, 3, True, 2]

Prog

(PARI) A067694(n) = if((2==n)||!n, 0, if(2==(n%4), 3, if(issquare(n), 1, 2))); \\ Antti Karttunen, Sep 27 2018

Crossrefs

Cf. A000700, A067731.

Sequence in context: A178412 A182598 A331084 * A131810 A365143 A233519

Adjacent sequences: A067691 A067692 A067693 * A067695 A067696 A067697

Keyword

easy,nonn

Author

Naohiro Nomoto, Feb 05 2002

Extensions

Edited by Dean Hickerson, Feb 15 2002

Status

approved