The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002186 Sprague-Grundy values for the game of Kayles (octal games .77 and .771). (Formerly M0410 N0156) 29
 0, 1, 2, 3, 1, 4, 3, 2, 1, 4, 2, 6, 4, 1, 2, 7, 1, 4, 3, 2, 1, 4, 6, 7, 4, 1, 2, 8, 5, 4, 7, 2, 1, 8, 6, 7, 4, 1, 2, 3, 1, 4, 7, 2, 1, 8, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 4, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 8, 6, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 8, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1, 8, 2, 7, 4, 1, 2, 8, 1, 4, 7, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Octal games 4.4, 4.41, 4.42, 4.43, 4.6, 4.61, 4.62 and 4.63 have values a(n-1). "The periodicity was first proved by R. K. Guy in 1949, the sequence necessarily being calculated by hand." [Beasley]. REFERENCES John D. Beasley, The Mathematics of Games, Dover Publ., Mineola, NY 2006, page 111. E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 91. Calkin, Neil J.; James, Kevin; Janoski, Janine E.; Leggett, Sarah; Richards, Bryce; Sitaraman, Nathan; and Thomas, Stephanie M.; Computing strategies for graphical Nim, in Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 171-185. (See page 174.) J. H. Conway, On Numbers and Games, Second Edition. A K Peters, Ltd, 2001, p. 128. R. K. Guy, "Anyone for Twopins?", in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. Guy, R. K. and Smith, C. A. B.; The G-values of various games. Proc. Cambridge Philos. Soc. 52 (1956), 514-526. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). 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..104. Sierra Brown, Spencer Daugherty, Eugene Fiorini, Barbara Maldonado, Diego Manzano-Ruiz, Sean Rainville, Riley Waechter, and Tony W. H. Wong, Nimber Sequences of Node-Kayles Games, J. Int. Seq., Vol. 23 (2020), Article 20.3.5. Achim Flammenkamp, Octal games R. K. Guy, Letters to N. J. A. Sloane, June-August 1968 R. K. Guy, Anyone for Twopins?, in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. [Annotated scanned copy, with permission] Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1). FORMULA From n=71 on, the sequence is periodic with period 12. The only exceptions are n=0, 3, 6, 9, 11, 15, 18, 21, 22, 28, 34, 39, 57 and 70. CROSSREFS Cf. A071074, A071434. Sequence in context: A242360 A299927 A006021 * A125936 A243614 A200942 Adjacent sequences: A002183 A002184 A002185 * A002187 A002188 A002189 KEYWORD nonn,nice,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 08 2001 Edited by Christian G. Bower, Oct 22 2002 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 August 12 09:11 EDT 2024. Contains 375085 sequences. (Running on oeis4.)