This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326880 BII-numbers of set-systems that are closed under nonempty intersection. 12
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 46, 47, 56, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 87, 88 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 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. The enumeration of these set-systems by number of covered vertices is A326881. LINKS EXAMPLE Most small numbers are in the sequence, but the sequence of non-terms together with the set-systems with those BII-numbers begins:   20: {{1,2},{1,3}}   22: {{2},{1,2},{1,3}}   28: {{1,2},{3},{1,3}}   30: {{2},{1,2},{3},{1,3}}   36: {{1,2},{2,3}}   37: {{1},{1,2},{2,3}}   44: {{1,2},{3},{2,3}}   45: {{1},{1,2},{3},{2,3}}   48: {{1,3},{2,3}}   49: {{1},{1,3},{2,3}}   50: {{2},{1,3},{2,3}}   51: {{1},{2},{1,3},{2,3}}   52: {{1,2},{1,3},{2,3}}   53: {{1},{1,2},{1,3},{2,3}}   54: {{2},{1,2},{1,3},{2,3}}   55: {{1},{2},{1,2},{1,3},{2,3}}   60: {{1,2},{3},{1,3},{2,3}}   61: {{1},{1,2},{3},{1,3},{2,3}}   62: {{2},{1,2},{3},{1,3},{2,3}}   84: {{1,2},{1,3},{1,2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; Select[Range[0, 100], SubsetQ[bpe/@bpe[#], Intersection@@@Select[Tuples[bpe/@bpe[#], 2], Intersection@@#!={}&]]&] CROSSREFS Cf. A006126, A048793, A102894, A102895, A102896, A102897, A306445, A326031, A326872, A326874, A326875, A326876, A326881. Sequence in context: A320249 A309066 A084981 * A078453 A052425 A272074 Adjacent sequences:  A326877 A326878 A326879 * A326881 A326882 A326883 KEYWORD nonn AUTHOR Gus Wiseman, Jul 29 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 15 15:01 EST 2019. Contains 329999 sequences. (Running on oeis4.)