cp's OEIS Frontend

A326784 BII-numbers of regular set-systems.

%I A326784 #5 Jul 27 2019 14:57:51
%S A326784 0,1,2,3,4,7,8,9,10,11,12,16,18,25,30,32,33,42,45,51,52,63,64,75,76,
%T A326784 82,94,97,109,115,116,127,128,129,130,131,132,136,137,138,139,140,144,
%U A326784 146,160,161,192,256,258,264,266,288,385,390,408,427,428,434,458
%N A326784 BII-numbers of regular set-systems.
%C A326784 A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. A set-system is regular if all vertices appear the same number of times.
%e A326784 The sequence of all regular set-systems together with their BII-numbers begins:
%e A326784    0: {}
%e A326784    1: {{1}}
%e A326784    2: {{2}}
%e A326784    3: {{1},{2}}
%e A326784    4: {{1,2}}
%e A326784    7: {{1},{2},{1,2}}
%e A326784    8: {{3}}
%e A326784    9: {{1},{3}}
%e A326784   10: {{2},{3}}
%e A326784   11: {{1},{2},{3}}
%e A326784   12: {{1,2},{3}}
%e A326784   16: {{1,3}}
%e A326784   18: {{2},{1,3}}
%e A326784   25: {{1},{3},{1,3}}
%e A326784   30: {{2},{1,2},{3},{1,3}}
%e A326784   32: {{2,3}}
%e A326784   33: {{1},{2,3}}
%e A326784   42: {{2},{3},{2,3}}
%e A326784   45: {{1},{1,2},{3},{2,3}}
%e A326784   51: {{1},{2},{1,3},{2,3}}
%t A326784 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A326784 Select[Range[0,100],SameQ@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]&]
%Y A326784 Cf. A000120, A001511, A005176, A029931, A048793, A070939, A295193, A322554, A326031, A326701, A326783 (uniform), A326785 (uniform regular).
%K A326784 nonn
%O A326784 1,3
%A A326784 _Gus Wiseman_, Jul 25 2019