

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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



