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A326788 BII-numbers of simple labeled graphs. 8
0, 4, 16, 20, 32, 36, 48, 52, 256, 260, 272, 276, 288, 292, 304, 308, 512, 516, 528, 532, 544, 548, 560, 564, 768, 772, 784, 788, 800, 804, 816, 820, 2048, 2052, 2064, 2068, 2080, 2084, 2096, 2100, 2304, 2308, 2320, 2324, 2336, 2340, 2352, 2356, 2560, 2564 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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 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.

Also numbers whose binary indices all belong to A018900.

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

The sequence of all simple labeled graphs together with their BII-numbers begins:

0: {}

4: {{1,2}}

16: {{1,3}}

20: {{1,2},{1,3}}

32: {{2,3}}

36: {{1,2},{2,3}}

48: {{1,3},{2,3}}

52: {{1,2},{1,3},{2,3}}

256: {{1,4}}

260: {{1,2},{1,4}}

272: {{1,3},{1,4}}

276: {{1,2},{1,3},{1,4}}

288: {{2,3},{1,4}}

292: {{1,2},{2,3},{1,4}}

304: {{1,3},{2,3},{1,4}}

308: {{1,2},{1,3},{2,3},{1,4}}

512: {{2,4}}

516: {{1,2},{2,4}}

528: {{1,3},{2,4}}

532: {{1,2},{1,3},{2,4}}

MATHEMATICA

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

Select[Range[0, 100], SameQ[2, ##]&@@Length/@bpe/@bpe[#]&]

CROSSREFS

Cf. A000120, A006125, A006129, A018900, A048793, A062880, A070939, A309356 (same for MM-numbers), A322551, A326031, A326702.

Other BII-numbers: A309314 (hyperforests), A326701 (set partitions), A326703 (chains), A326704 (antichains), A326749 (connected), A326750 (clutters), A326751 (blobs), A326752 (hypertrees), A326754 (covers).

Sequence in context: A071966 A349521 A326781 * A039943 A193996 A232400

Adjacent sequences: A326785 A326786 A326787 * A326789 A326790 A326791

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 25 2019

STATUS

approved

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Last modified January 29 15:13 EST 2023. Contains 359923 sequences. (Running on oeis4.)