A006016 The nim value for the game of Sym with n tails and 1 head. (Formerly M0935)

1, 2, 4, 3, 6, 7, 8, 16, 18, 25, 32, 11, 64, 31, 128, 10, 256, 5, 512, 28, 1024, 34, 2048, 47, 4096, 85

Offset

0,2

Comments

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

References

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 441.

D. E. Knuth, The TeXbook, p. 241.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..25.

R. K. Guy, She Loves Me, She Loves Me Not: Relatives of Two Games of Lenstra, 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]

Crossrefs

Sequence in context: A320672 A367262 A358467 * A227413 A217122 A239622

Adjacent sequences: A006013 A006014 A006015 * A006017 A006018 A006019

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Knuth reference from R. K. Guy, Mar 15 2003

a(21)-a(25) from Sean A. Irvine, Dec 05 2016

Title improved by Sean A. Irvine, Dec 05 2016

Status

approved