

A164950


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


1



1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0
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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.
Martin Gardner, Mathematical games : of sprouts and brussels sprouts, games with a topological flavor, Scientific American 217 (July 1967), 112115.


LINKS

Table of n, a(n) for n=1..20.
D. Applegate, G. Jacobson, and D. Sleator, Computer Analysis of Sprouts, Tech. Report CMUCS91144, Carnegie Mellon University Computer Science Technical Report, 1991.
Julien Lemoine, Simon Viennot, Analysis of misère Sprouts game with reduced canonical trees, arXiv:0908.4407 [math.CO], 2009.
Julien Lemoine, Simon Viennot, Records / Misère Sprouts, SproutsWiki
Wikipedia, Sprouts


CROSSREFS

Cf. A164951.
Sequence in context: A159638 A187615 A120528 * A068433 A088592 A029692
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



