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

%I #9 Sep 27 2018 17:53:59

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A067694/b067694.txt">Table of n, a(n) for n = 0..65537</a>

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

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

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

%Y Cf. A000700, A067731.

%K easy,nonn

%O 0,4

%A _Naohiro Nomoto_, Feb 05 2002

%E Edited by _Dean Hickerson_, Feb 15 2002

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