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A014586 Nim-Grundy function for Take-a-Square (or Subtract-a-Square) game. 2
0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 3, 2, 3, 4, 0, 1, 2, 3, 2, 0, 1, 2, 3, 2, 0, 1, 2, 3, 2, 3, 4, 5, 0, 1, 3, 4, 5, 0, 1, 3, 4, 5, 0, 1, 3, 0, 1, 0, 1, 2, 4, 3, 0, 1, 5, 6, 2, 3, 4, 5, 6, 2, 3, 4, 5, 0, 1, 6, 3, 2, 4, 2, 6, 4, 5, 0, 1, 6, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

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.

PROG

(Sage)

def A014586(max) :

....res = []

....for i in xrange(max+1) :

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

........k = len(moves)

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

........res.append(mex)

....return res

end # Eric M. Schmidt, Jul 20 2013

CROSSREFS

Sequence in context: A298307 A287002 A119346 * A122924 A133450 A029410

Adjacent sequences:  A014583 A014584 A014585 * A014587 A014588 A014589

KEYWORD

nonn

AUTHOR

Achim Flammenkamp (achim(AT)HRZ.Uni-Bielefeld.DE)

STATUS

approved

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Last modified November 12 16:50 EST 2018. Contains 317116 sequences. (Running on oeis4.)