

A327041


a(n) is the number whose binary indices are the union of the setsystem with BIInumber n.


19



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
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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 setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. Every setsystem has a different BIInumber. 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 BIInumber of {{2},{1,3}} is 18.


LINKS

Table of n, a(n) for n=0..86.


EXAMPLE

22 is the BIInumber 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.
Cf. A000120, A001511, A029931, A035327, A048793, A070939, A072639, A326031, A326702, A326947.
Sequence in context: A194225 A025782 A120506 * A277267 A246262 A275974
Adjacent sequences: A327038 A327039 A327040 * A327042 A327043 A327044


KEYWORD

nonn


AUTHOR

Gus Wiseman, Aug 19 2019


STATUS

approved



