This site is supported by donations to The OEIS Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A164950 1 if there is a winning strategy for misère Sprouts with n initial points, else 0. 2
1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)



This comes from changing "W" to "1" and "L" to "0" in Figure 1, p.2 of Lemoine. For the number of different canonical trees in game trees obtained from a starting position, see A164950. Sprouts is a two-player topological game, invented in 1967 by Michael Paterson and John Conway. The game starts with p spots, lasts at most 3p-1 moves, and the player who makes the last move wins. In the misere version of Sprouts, on the contrary, the player who makes the last move loses.

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


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.

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), 112-115.


Table of n, a(n) for n=1..17.

Julien Lemoine, Simon Viennot, Analysis of misère Sprouts game with reduced canonical trees, Aug 30, 2009.


Cf. A164950.

Sequence in context: A159638 A187615 A120528 * A068433 A088592 A029692

Adjacent sequences:  A164947 A164948 A164949 * A164951 A164952 A164953




Jonathan Vos Post, Sep 01 2009



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified October 21 11:34 EDT 2017. Contains 293693 sequences.