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%I #32 Apr 20 2022 21:23:17
%S 0,1,2,2,3,3,4,3,4,4,5,4,5,5,5,4,5,5,6,5,6,6,6,5,6,6,6,6,7,6,7,5,6,6,
%T 7,6,7,7,7,6,7,7,7,7,7,7,8,6,7,7,7,7,8,7,8,7,8,8,8,7,8,8,8,6,7,7,8,7,
%U 8,8,8,7,8,8,8,8,8,8,9,7,8,8,8,8,8,8,9,8,9,8,9,8,9,9,9,7,8,8,8,8,9,8,9,8,9
%N Minimal number of points needed to make a topology having n open sets.
%C Differs from A003313 first at a(71) = 8, where A003313(71) = 9, and then at indices n = 139, 141, 142, .... - _M. F. Hasler_, Apr 20 2022
%D M. Erné and K. Stege, Counting finite posets and topologies, Tech. Report 236, University of Hannover, 1990.
%H Achim Flammenkamp, <a href="/A137813/b137813.txt">Table of n, a(n) for n = 1..2790</a>
%H M. Erné and K. Stege, <a href="http://dx.doi.org/10.1007/BF00383446">Counting finite posets and topologies</a>, Order, September 1991, Volume 8, Issue 3, pp 247-265.
%H K. Ragnarsson and B. E. Tenner, <a href="http://dx.doi.org/10.1016/j.jcta.2009.05.002">Obtainable sizes of topologies on finite sets</a>, J. Combin. Theory Ser. A 117 (2010) 138-151.
%e A topology having 7 open sets can be made on 4 points. The open sets are: {}, {1}, {2}, {1,2}, {1,3}, {1,2,3}, {1,2,3,4}. No topology having 7 open sets can be made with fewer points.
%Y Cf. A137814.
%K nonn
%O 1,3
%A _Bridget Tenner_, Feb 11 2008
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