A164950 1 if there is a winning strategy for misère Sprouts with n initial points, else 0.

1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0

Offset

1,1

Comments

This comes from changing "W" to "1" and "L" to "0" in Figure 1, p. 2 of Lemoine & Viennot's paper.

Lemoine & Viennot conjecture that, for n > 4, a(n) = 1 if and only if n is 0, 4, or 5 mod 6. - Charles R Greathouse IV, Dec 13 2012

References

Elwyn Berkelamp, John Conway, and Richard Guy, Winning ways for your mathematical plays, A K Peters, 2001.

Links

Table of n, a(n) for n=1..20.

D. Applegate, G. Jacobson, and D. Sleator, Computer Analysis of Sprouts, Tech. Report CMU-CS-91-144, Carnegie Mellon University Computer Science Technical Report, 1991.

Martin Gardner, Mathematical games: Of sprouts and brussels sprouts, games with a topological flavor, Scientific American 217 (July 1967), 112-115.

Julien Lemoine and Simon Viennot, Analysis of misère Sprouts game with reduced canonical trees, arXiv:0908.4407 [math.CO], 2009.

Julien Lemoine and Simon Viennot, Records / Misère Sprouts, SproutsWiki

Wikipedia, Sprouts

Crossrefs

Cf. A164951.

Sequence in context: A120528 A287663 A195376 * A068433 A266895 A088592

Adjacent sequences: A164947 A164948 A164949 * A164951 A164952 A164953

Keyword

nonn,hard,more

Author

Jonathan Vos Post, Sep 01 2009

Extensions

a(18)-a(20) from Andrey Zabolotskiy, Feb 19 2018 from SproutsWiki

Status

approved