

A327103


Minimum vertexdegree in the setsystem with BIInumber n.


17



0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2
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OFFSET

0,8


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 (finite set of finite nonempty sets) 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. Elements of a setsystem are sometimes called edges.
In a setsystem, the degree of a vertex is the number of edges containing it.


LINKS

Table of n, a(n) for n=0..87.


EXAMPLE

The BIInumber of {{2},{3},{1,2},{1,3},{2,3}} is 62, and its degrees are (2,3,3), so a(62) = 2.


MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[If[n==0, 0, Min@@Length/@Split[Sort[Join@@bpe/@bpe[n]]]], {n, 0, 100}]


CROSSREFS

The maximum vertexdegree is A327104.
Positions of 1's are A327105.
Positions of terms > 1 are A327107.
Cf. A000120, A048793, A058891, A070939, A326031, A326701, A326783, A326786, A327041, A327228, A327229.
Sequence in context: A113515 A103754 A058665 * A290105 A191898 A043290
Adjacent sequences: A327100 A327101 A327102 * A327104 A327105 A327106


KEYWORD

nonn


AUTHOR

Gus Wiseman, Aug 26 2019


STATUS

approved



