Some interesting sequences

[David W. Wilson]

 Here are some interesting sequences of partition numbers mod 11.  No other
number seems to give such interesting results relative the partitions.

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%I A000000
%S A000000 1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,6,6,6,
%T A000000 7,7,7,7,8,8,9,9,10,10,0,0,1,1,2,2,3,3,4,5,6,6,7,7,9,9,10,0,1,2,3,4,5,6,
%U A000000 8,8,10,0,1,2,4,5,7,8,10,0,2,3,6,7,9,0,2,4,7,8,0,2,5,6,10,1,4,6,10,1,5,7
%N A000000 partition(11n) mod 11
%A A000000 David Wilson (wilson at ctron.com)
%O 0,11

%I A000001
%S A000001 1,0,1,1,1,0,1,0,1,1,1,1,2,1,1,1,2,1,2,1,2,2,2,2,3,2,3,3,3,3,4,3,4,3,4,4,
%T A000001 5,4,5,5,6,5,7,6,7,7,7,7,9,8,9,9,10,9,0,10,1,0,2,1,3,2,4,4,5,5,7,6,8,8,9,
%U A000001 9,1,0,2,2,4,3,6,5,8,8,10,10,2,1,4,4,7,6,10,9,2,2,5,5,9,8,1,2,5,5,10,9,3
%N A000001 partition(11n+1) mod 11
%A A000001 David Wilson (wilson at ctron.com)
%O 0,13

%I A000002
%S A000002 2,2,2,0,2,2,2,2,2,2,2,2,4,2,4,2,4,4,4,4,4,6,6,4,6,6,6,6,8,8,8,8,10,8,10,
%T A000002 10,1,1,1,1,3,3,5,3,5,5,7,7,9,9,0,0,2,2,4,4,6,6,8,8,1,1,3,3,7,7,9,9,2,2,
%U A000002 6,6,10,10,3,3,7,9,0,2,6,8,1,1,7,9,2,2,8,10,5,7,2,2,8,10,7,9,4,6,3,5,2,4
%N A000002 partition(11n+2) mod 11
%A A000002 David Wilson (wilson at ctron.com)
%O 0,1

%I A000003
%S A000003 3,3,0,3,3,0,3,3,3,3,3,3,3,3,3,6,6,3,6,6,6,6,6,6,9,9,6,9,9,9,1,1,1,1,1,1,
%T A000003 4,4,4,7,7,7,7,10,10,10,2,10,5,5,5,8,8,8,0,0,3,6,6,6,1,1,1,4,7,7,10,2,2,
%U A000003 5,8,0,3,6,6,1,4,4,10,2,5,8,0,3,9,1,4,10,5,5,3,6,9,4,10,2,0,3,9,7,2,5,3
%N A000003 partition(11n+3) mod 11
%A A000003 David Wilson (wilson at ctron.com)
%O 0,1

%I A000004
%S A000004 5,0,5,0,5,0,5,0,5,5,5,0,5,5,5,5,5,5,10,5,10,5,10,5,10,5,4,10,4,10,4,10,
%T A000004 4,4,4,4,9,4,9,9,3,9,3,9,8,3,8,3,2,8,2,8,7,2,1,7,1,1,6,1,0,6,5,0,10,5,4,
%U A000004 10,9,4,3,9,2,3,7,2,1,7,0,6,10,5,4,10,3,9,2,8,1,7,5,6,4,10,3,9,7,2,0,6,4
%N A000004 partition(11n+4) mod 11
%A A000004 David Wilson (wilson at ctron.com)
%O 0,1

%I A000005
%S A000005 7,0,7,0,0,7,7,0,7,0,7,7,7,0,7,7,7,7,3,7,3,7,7,7,3,3,3,3,3,3,10,3,10,3,
%T A000005 10,10,6,10,6,10,6,6,2,6,2,2,2,2,9,2,5,9,5,5,1,5,8,1,8,8,4,8,0,4,0,7,3,7,
%U A000005 10,3,6,10,2,6,9,9,5,5,8,1,0,4,7,7,10,3,2,6,9,9,8,1,0,4,7,3,2,6,5,5,4,4
%N A000005 partition(11n+5) mod 11
%A A000005 David Wilson (wilson at ctron.com)
%O 0,1

%I A000007
%S A000007 4,0,0,4,0,0,4,0,4,4,0,0,4,0,4,4,4,4,4,4,4,4,4,4,8,4,4,8,8,4,8,8,8,1,8,8,
%T A000007 1,8,1,1,1,1,5,1,5,5,5,5,9,5,9,9,9,9,2,2,6,6,6,6,10,6,10,3,3,3,7,3,7,0,0,
%U A000007 0,8,4,8,1,1,1,9,5,2,2,2,6,3,10,3,7,0,0,8,8,1,5,9,9,10,6,3,7,0,0,1,1,9,2
%N A000007 partition(11n+7) mod 11
%A A000007 David Wilson (wilson at ctron.com)
%O 0,1

%I A000008
%S A000008 0,6,5,0,0,6,0,0,0,0,0,0,0,6,0,0,0,0,0,6,0,6,0,0,0,6,0,0,0,6,0,6,0,6,0,6,
%T A000008 6,6,0,6,6,6,0,6,0,6,6,6,6,1,6,6,6,1,6,1,6,1,6,1,6,7,6,1,1,7,1,7,1,7,1,7,
%U A000008 1,2,1,2,7,2,7,2,7,8,7,8,2,3,2,8,8,3,8,9,8,9,3,9,3,4,3,4,9,10,9,5,4,5,10
%N A000008 partition(11n+8) mod 11
%A A000008 David Wilson (wilson at ctron.com)
%O 0,2

%I A000009
%S A000009 8,0,0,0,8,0,0,8,8,0,0,0,8,0,8,8,8,0,8,8,8,8,8,8,8,8,8,8,5,8,5,8,5,5,5,5,
%T A000009 2,5,5,5,2,5,2,2,10,2,2,2,10,10,10,10,7,10,7,7,4,7,4,4,1,4,1,1,9,1,9,9,6,
%U A000009 9,3,6,0,3,0,0,8,8,5,5,2,2,10,2,4,7,4,4,9,1,6,6,0,3,8,8,2,5,10,10,4,7,9
%N A000009 partition(11n+9) mod 11
%A A000009 David Wilson (wilson at ctron.com)
%O 0,1

%I A000010
%S A000010 9,0,0,0,0,9,9,0,0,0,9,0,9,0,0,9,9,9,9,0,9,9,9,9,9,9,9,9,9,9,7,9,7,7,7,7,
%T A000010 7,7,7,7,5,7,5,7,5,5,5,5,3,5,3,3,3,3,1,1,1,1,1,1,8,10,10,10,8,8,6,8,6,6,
%U A000010 4,4,2,4,2,2,0,0,9,0,7,7,5,5,3,3,1,1,10,10,6,8,6,4,2,2,9,0,7,7,3,3,10,1
%N A000010 partition(11n+10) mod 11
%A A000010 David Wilson (wilson at ctron.com)
%O 0,1