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

Author

Naohiro Nomoto, Feb 05 2002

Keywords

• easy
• nonn

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

Crossrefs

Cf. A000700, A067731.

Programs

Mathematica

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

PARI

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

Formula

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

Extensions

Edited by Dean Hickerson, Feb 15 2002