The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A361517 The value of n for which the two-player impartial {0,1}-Toggle game on a generalized Petersen graph GP(n,2) with a (1,0)-weight assignment is a next-player winning game. 3
 3, 4, 5, 11, 17, 27, 35, 37, 49, 59, 69, 81, 91, 103, 115, 123, 135, 137, 167, 175, 189, 199, 207, 287, 295, 307, 361, 1051, 2507, 2757, 2917, 3057, 3081, 7255, 7361, 7871, 16173 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS The two-player impartial {0,1}-Toggle game is played on a simple connected graph G where each vertex is assigned an initial weight of 0 or 1. A Toggle move consists of selecting a vertex v and switching its weight as well as the weights of each of its neighbors. This move is only legal provided the weight of vertex v is 1 and the total sum of the vertex weights decreases. In the special case G=GP(n,2), a (1,0)-weight assignment is one in which each vertex of the outer polygon is assigned weight 1 and each vertex of the inner polygon(s) is assigned weight 0. REFERENCES E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001. LINKS Table of n, a(n) for n=3..39. E. Fiorini, M. Lind, A. Woldar, and T. W. H. Wong, Characterizing Winning Positions in the Impartial Two-Player Pebbling Game on Complete Graphs, Journal of Integer Sequences, 24(6), 2021. Katherine Levandosky, CGSuite Program. EXAMPLE For n = 3, the {0,1}-Toggle game on GP(3,2) with a (1,0)-weight assignment is a next-player winning game. For n = 5, the {0,1}-Toggle game on GP(5,2) with a (1,0)-weight assignment is a next-player winning game. PROG (CGSuite) # See Levandosky link CROSSREFS Cf. A071426, A340631, A346197, A346401, A346637. Sequence in context: A362665 A293713 A280255 * A276542 A318077 A074221 Adjacent sequences: A361514 A361515 A361516 * A361518 A361519 A361520 KEYWORD nonn,more AUTHOR Eugene Fiorini, Maxwell Fogler, Katherine Levandosky, Bryan Lu, Jacob K. Porter and Andrew Woldar, Mar 14 2023 STATUS approved

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

Last modified May 21 08:47 EDT 2024. Contains 372732 sequences. (Running on oeis4.)