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%I M0935 #27 May 02 2023 12:50:12
%S 1,2,4,3,6,7,8,16,18,25,32,11,64,31,128,10,256,5,512,28,1024,34,2048,
%T 47,4096,85
%N The nim value for the game of Sym with n tails and 1 head.
%C Consider a row of n coins. In the game of Sym players take turns at turning over any symmetric arrangement of coins with the restriction that the rightmost coin turned over must be heads. The winner is the last player to move. This sequence gives the nim value for an initial arrangement consisting of n tails followed by 1 head, thus a(0)=1 is for a single coin starting on heads. In fact, with this starting arrangement the first player can always win by simply turning over the single head. Some nim values for small n are T=0, H=1, TH=2, HH=3, TTH=4, THH=6, HTH=5, HHH=7, TTTH=3, and so on. - _Sean A. Irvine_, Dec 05 2016
%D E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 441.
%D D. E. Knuth, The TeXbook, p. 241.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. K. Guy, <a href="/A006016/a006016_1.pdf">She Loves Me, She Loves Me Not: Relatives of Two Games of Lenstra</a>, in "Een Pak Met Een Korte Broek" [“A Book in Short Trousers"], ed. P. van Emde Boas et al., Privately Printed, Amsterdam, May 18, 1977 (unnumbered pages). [Cached copy, with permission]
%K nonn,more
%O 0,2
%A _N. J. A. Sloane_
%E Knuth reference from _R. K. Guy_, Mar 15 2003
%E a(21)-a(25) from _Sean A. Irvine_, Dec 05 2016
%E Title improved by _Sean A. Irvine_, Dec 05 2016
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