cp's OEIS Frontend

A326783 BII-numbers of uniform set-systems.

%I A326783 #7 Jul 27 2019 14:57:51
%S A326783 0,1,2,3,4,8,9,10,11,16,20,32,36,48,52,64,128,129,130,131,136,137,138,
%T A326783 139,256,260,272,276,288,292,304,308,512,516,528,532,544,548,560,564,
%U A326783 768,772,784,788,800,804,816,820,1024,1088,2048,2052,2064,2068,2080
%N A326783 BII-numbers of uniform set-systems.
%C A326783 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 uniform if all edges have the same size.
%C A326783 Alternatively, these are numbers whose binary indices all have the same binary weight, where the binary weight of a nonnegative integer is the numbers of 1's in its binary digits.
%e A326783 The sequence of all uniform set-systems together with their BII-numbers begins:
%e A326783     0: {}
%e A326783     1: {{1}}
%e A326783     2: {{2}}
%e A326783     3: {{1},{2}}
%e A326783     4: {{1,2}}
%e A326783     8: {{3}}
%e A326783     9: {{1},{3}}
%e A326783    10: {{2},{3}}
%e A326783    11: {{1},{2},{3}}
%e A326783    16: {{1,3}}
%e A326783    20: {{1,2},{1,3}}
%e A326783    32: {{2,3}}
%e A326783    36: {{1,2},{2,3}}
%e A326783    48: {{1,3},{2,3}}
%e A326783    52: {{1,2},{1,3},{2,3}}
%e A326783    64: {{1,2,3}}
%e A326783   128: {{4}}
%e A326783   129: {{1},{4}}
%e A326783   130: {{2},{4}}
%e A326783   131: {{1},{2},{4}}
%t A326783 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A326783 Select[Range[0,100],SameQ@@Length/@bpe/@bpe[#]&]
%Y A326783 Cf. A000120, A029931, A048793, A070939, A047966, A306017, A306021, A319269, A320324, A326031, A326784 (regular), A326785 (uniform regular), A326788.
%K A326783 nonn
%O A326783 1,3
%A A326783 _Gus Wiseman_, Jul 25 2019