OFFSET

0,5

COMMENTS

Concerning the January 1997 dissertation of Achim Flammenkamp, his home page (currently http://wwwhomes.uni-bielefeld.de/cgi-bin/cgiwrap/achim/index.cgi) has the link shown below, and a comment that a book was published in July 1997 by Hans-Jacobs-Verlag, Lage, Germany with the title Lange Perioden in Subtraktions-Spielen (ISBN 3-932136-10-1). This is an enlarged study (more than 200 pages) of his dissertation. - N. J. A. Sloane, Jul 25 2019

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E26.

W. W. Rouse Ball and H. S. M. Coxeter, Mathematical Recreations and Essays, 12th Edition.

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 0..10000 (corrected by Eric M. Schmidt, Apr 23 2019)

David Eppstein, Faster Evaluation of Subtraction Games, Proceedings of the 9th International Conference on Fun with Algorithms (FUN 2018), Leibniz International Proceedings in Informatics, arXiv:1804.06515 [cs.DS], 2018.

Achim Flammenkamp, Lange Perioden in Subtraktions-Spielen, Dissertation, Dept. Math., University of Bielefeld, Germany.

Sean A. Irvine, Java program (github)

Wikipedia, Sprague-Grundy theorem

FORMULA

a(n) = 0 iff n belongs to A030193. - Rémy Sigrist, May 30 2019

PROG

(Sage)

def A014586_list(max) :

res = []

for i in range(max+1) :

moves = list({res[i-r^2] for r in range(1, isqrt(i)+1)})

moves.sort()

k = len(moves)

mex = next((j for j in range(k) if moves[j] != j), k)

res.append(mex)

return res

A014586_list(100)

# Eric M. Schmidt, Jul 20 2013, corrected Eric M. Schmidt, Apr 23 2019

CROSSREFS

KEYWORD

nonn

AUTHOR

STATUS

approved