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%I M2455 #15 Oct 21 2023 16:59:46
%S 0,1,3,5,9,17,35,79,209
%N Maximum of minimum total weight for threshold functions of n Boolean variables.
%D S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 268.
%D S. Muroga, T. Tsuboi and C. R. Baugh, "Enumeration of threshold functions of eight variables," IEEE Transactions on Computers, 19 (1970), 818-825.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Noga Alon and Van H. Vu, <a href="https://doi.org/10.1006/jcta.1997.2780">Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs</a>, Journal of Combinatorial Theory, Series A, Volume 79, Issue 1, July 1997, Pages 133-160.
%F For asymptotics see the Alon-Vu article.
%e a(4)=9 because the threshold functions "majority of wwxxyz000" and "majority of wwwxxyz00" and "majority of wwwxxyyz0" cannot be described as majority of seven or five things, but no threshold function of w,x,y,z requires a majority of more than nine.
%K nonn,hard,more
%O 0,3
%A _N. J. A. Sloane_