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A327041
a(n) is the number whose binary indices are the union of the set-system with BII-number n.
20
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, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
OFFSET
0,3
COMMENTS
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.
EXAMPLE
22 is the BII-number of {{2},{1,2},{1,3}}, and 7 has binary indices {1,2,3}, so a(22) = 7.
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Total[2^Union@@bpe/@bpe[n]]/2, {n, 0, 100}]
CROSSREFS
Indices of records are A253317.
Sequence in context: A194225 A025782 A120506 * A277267 A246262 A275974
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 19 2019
STATUS
approved