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A327041 a(n) is the number whose binary indices are the union of the set-system with BII-number n.

%I A327041 #12 May 28 2024 01:32:37
%S A327041 0,1,2,3,3,3,3,3,4,5,6,7,7,7,7,7,5,5,7,7,7,7,7,7,5,5,7,7,7,7,7,7,6,7,
%T A327041 6,7,7,7,7,7,6,7,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
%U A327041 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7
%N A327041 a(n) is the number whose binary indices are the union of the set-system with BII-number n.
%C A327041 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. Every set-system has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18.
%H A327041 Tilman Piesk, <a href="https://commons.wikimedia.org/wiki/File:OR_and_XOR_of_binary_exponents.svg">Illustration of the first 128 terms</a>
%e A327041 22 is the BII-number of {{2},{1,2},{1,3}}, and 7 has binary indices {1,2,3}, so a(22) = 7.
%t A327041 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A327041 Table[Total[2^Union@@bpe/@bpe[n]]/2,{n,0,100}]
%Y A327041 Indices of records are A253317.
%Y A327041 Cf. A000120, A001511, A029931, A035327, A048793, A070939, A072639, A326031, A326702, A326947, A261283 (XOR equivalent).
%K A327041 nonn
%O A327041 0,3
%A A327041 _Gus Wiseman_, Aug 19 2019