This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A286874 #69 Jul 29 2025 18:24:03
%S A286874 1,2,2,3,4,5,6,7,8,12,13,17,20,26
%N A286874 Maximal number of binary vectors of length n such that the union (or bitwise OR) of any 2 distinct vectors does not contain any other vector.
%C A286874 The concatenation of these vectors produces a 2-disjunct matrix.
%C A286874 a(10) >= 13. Here is a candidate solution: {0101000001 0001000110 1000100001 0010000011 1001010000 0010110000 1000001010 0011001000 0100100010 1110000000 0100010100 0000011001 0000101100}. - _Dmitry Kamenetsky_, Sep 07 2017
%C A286874 a(11) >= 17. Here is a candidate solution: {01000010100 10000100100 00000001110 00010010001 10000011000 01000001001 00001010010 00010101000 00100110000 00100000101 00000100011 00101001000 10110000000 11000000010 00011000100 10001000001 01001100000}. - _Dmitry Kamenetsky_, Sep 07 2017
%C A286874 The best lower bounds known for the next terms a(14)-a(16) are 28, 40 (corrected by _Steinar H. Gunderson_, Jul 22 2025) and 45 (see attached files for the solutions).
%C A286874 The bounds for a(10) and a(11) are tight, by the Z3 SMT solver. - _Steinar H. Gunderson_, Jun 23 2025
%C A286874 a(12)-a(13) were determined by exhaustive parallel search. - _Steinar H. Gunderson_, Jul 17 2025
%H A286874 Johan V. Dinesen, <a href="/A286874/a286874_1.txt">Lower bound and solution for a(15)</a>
%H A286874 P. Erdös, P. Frankl and Z. Füredi, <a href="https://doi.org/10.1016/0097-3165(82)90004-8">Families of finite sets in which no set is covered by the union of two others</a>, J. Combin. Theory, A33 (1982), 158-166.
%H A286874 Dmitry Kamenetsky, <a href="/A286874/a286874.txt">Lower bounds and their solutions for a(12-16)</a>
%H A286874 W. Kautz and R. Singleton, <a href="https://doi.org/10.1109/TIT.1964.1053689">Nonrandom binary superimposed codes</a>, IEEE Transactions on Information Theory, Volume: 10, Issue: 4, October 1964.
%H A286874 Wikipedia, <a href="https://en.wikipedia.org/wiki/Disjunct_matrix">Disjunct Matrix</a>
%H A286874 Wikipedia, <a href="https://en.wikipedia.org/wiki/Superimposed_code">Superimposed code</a>
%e A286874 Here is a solution for n=9: {110001000 001001010 001100100 100100010 100010100 000010011 101000001 011010000 000111000 010100001 010000110 000001101}.
%Y A286874 Cf. A054961, A303977 gives the number of distinct solutions.
%K A286874 nonn,hard,more
%O A286874 0,2
%A A286874 _Dmitry Kamenetsky_, Aug 02 2017
%E A286874 a(10)-a(11) from _Zhao Hui Du_, May 04 2018
%E A286874 a(12)-a(13) from _Steinar H. Gunderson_, Jul 17 2025