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%I #25 Jul 12 2019 14:10:13
%S 0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3
%N Baron Munchhausen's Omni-Sequence.
%C a(n) is the minimal number of weighings necessary to differentiate unlabeled coins of weight 1, 2, ..., n grams on a two-pan balance. See the Khovanova-Lewis paper for more information.
%C We have 3 <= a(n) <= 4 for 20 <= n <= 26 and a(n) = 4 for 27 <= n <= 58.
%C In general, log_3(n) <= a(n) <= 2log_2(n).
%H M. Brand, <a href="https://doi.org/10.1016/j.disc.2011.12.026">Tightening the bounds on the Baron's Omni-sequence</a>, Discrete Math., 312 (2012), 1326-1335.
%H Michael Brand, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i4p40">Munchhausen Matrices</a>, Electronic Journal of Combinatorics, Vol. 19 (2012) #P40.
%H Michael Brand, <a href="https://arxiv.org/abs/1304.7075">Lower bounds on the Munchhausen problem</a>, arXiv preprint arXiv:1304.7075 [cs.IT], 2013.
%H Michael Brand, <a href="https://ajc.maths.uq.edu.au/pdf/59/ajc_v59_p081.pdf">Lower bounds on the Münchhausen problem</a>, Australasian Journal of Combinatorics, Volume 59(1) (2014), Pages 81-85.
%H T. Khovanova, <a href="http://blog.tanyakhovanova.com/?p=148">Coins Sequence</a>
%H T. Khovanova, <a href="http://blog.tanyakhovanova.com/?p=250">My First Polymath Project</a>
%H T. Khovanova and J. B. Lewis, <a href="http://www.combinatorics.org/Volume_18/Abstracts/v18i1p37.html">Baron Munchhausen Redeems Himself: Bounds for a Coin-Weighing Puzzle</a>, Electronic J. Combinatorics 18 (2011) P37.
%e For n = 6, the weighings 6 = 1 + 2 + 3 and 1 + 6 < 3 + 5 uniquely identify the six coins 1, 2, 3, 4, 5, 6.
%Y Cf. A174541.
%K hard,nonn,more
%O 1,3
%A _Tanya Khovanova_ and _Joel B. Lewis_, Feb 17 2011
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