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A327106 BII-numbers of set-systems with maximum degree 2. 2
5, 6, 7, 13, 14, 15, 17, 19, 20, 22, 24, 25, 26, 27, 28, 30, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 65, 66, 67, 68, 72, 73, 74, 75, 76, 80, 82, 96, 97, 133, 134, 135, 141, 142, 143, 145, 147, 148, 150, 152, 153, 154, 155, 156, 158, 162 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 (finite set of finite nonempty sets) 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. Elements of a set-system are sometimes called edges.

In a set-system, the degree of a vertex is the number of edges containing it.

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

The sequence of all set-systems with maximum degree 2 together with their BII-numbers begins:

   5: {{1},{1,2}}

   6: {{2},{1,2}}

   7: {{1},{2},{1,2}}

  13: {{1},{1,2},{3}}

  14: {{2},{1,2},{3}}

  15: {{1},{2},{1,2},{3}}

  17: {{1},{1,3}}

  19: {{1},{2},{1,3}}

  20: {{1,2},{1,3}}

  22: {{2},{1,2},{1,3}}

  24: {{3},{1,3}}

  25: {{1},{3},{1,3}}

  26: {{2},{3},{1,3}}

  27: {{1},{2},{3},{1,3}}

  28: {{1,2},{3},{1,3}}

  30: {{2},{1,2},{3},{1,3}}

  34: {{2},{2,3}}

  35: {{1},{2},{2,3}}

  36: {{1,2},{2,3}}

  37: {{1},{1,2},{2,3}}

MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

Select[Range[0, 100], If[#==0, 0, Max@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]]==2&]

CROSSREFS

Positions of 2's in A327104.

Graphs with maximum degree 2 are counted by A136284.

Cf. A000120, A048793, A058891, A070939, A326031, A326701, A326786, A327041, A327103.

Sequence in context: A011761 A106745 A165776 * A003273 A006991 A047574

Adjacent sequences:  A327103 A327104 A327105 * A327107 A327108 A327109

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 26 2019

STATUS

approved

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Last modified November 13 10:29 EST 2019. Contains 329093 sequences. (Running on oeis4.)