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%I #25 Jan 17 2024 15:04:02
%S 1,4,8,16
%N Numbers k such that a triplewhist tournament TWh(k) exists.
%C The present state of knowledge, quoting from Ge (2007), is that a TWh(k) exists iff k == 0 or 1 (mod 4), except for k = 5, 9, 12, 13 and possibly 17.
%C After 16, the sequence continues 17?, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, ...
%H G. Ge and C. W. H. Lam, <a href="https://doi.org/10.1016/S0097-3165(02)00018-3">Some new triplewhist tournaments TWh(v)</a>, J. Combinat. Theory, A101 (2003), 153-159.
%H Gennian Ge, <a href="https://doi.org/10.1016/j.jcta.2007.01.012">Triplewhist tournaments with the three person property</a>, J. Combinat. Theory, A114 (2007), 1438-1455.
%H Harri Haanpää and Petteri Kaski, <a href="http://lib.tkk.fi/Diss/2004/isbn9512269422/article3.pdf">The near resolvable 2-(13,4,3) designs and thirteen-player whist tournaments</a> [shows that no TWh(13) exists]
%K nonn,more,bref,nice
%O 1,2
%A _N. J. A. Sloane_, Oct 16 2003
%E Of course this entry is much too short. But I have included it in the hope that this will encourage someone to settle the question of whether a(5) is 17 or 20 - i.e., does a TWh(17) exist?
%E Link supplied by _Jon E. Schoenfield_, Aug 01 2006
%E Edited by _Andrey Zabolotskiy_, Jan 17 2024
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