

A014587


Nim function for TakeaFactorialGame (a subtraction game).


3



0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2
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OFFSET

0,3


COMMENTS

Concerning the January 1997 dissertation of Achim Flammenkamp, his home page (currently http://wwwhomes.unibielefeld.de/cgibin/cgiwrap/achim/index.cgi) has the link shown below, and a comment that a book was published in July 1997 by HansJacobsVerlag, Lage, Germany with the title Lange Perioden in SubtraktionsSpielen (ISBN 3932136101). 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.


LINKS

Eric M. Schmidt, Table of n, a(n) for n = 0..10000
Achim Flammenkamp, Lange Perioden in SubtraktionsSpielen, Dissertation, Dept. Math., University of Bielefeld, Germany.


FORMULA

Conjecture: Appears to be periodic with period of length 25 = [0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3] starting with the initial term (there is no preamble).  Michel Dekking, Jul 26 2019
This conjecture is false, because moving from 10! = 3628800 to 0 is a legal move, and so a(3628800) cannot be zero. A similar argument shows that for no value of P is this sequence periodic with period P starting at term 0 (for a(P!) cannot be zero).  Nathan Fox, Jul 28 2019.


PROG

(Sage)
def A014587(max) :
res = []
fact = [1]
while fact[1] <= max : fact.append(factorial(len(fact)))
for i in range(max+1) :
moves = list({res[if] for f in fact if f <= i})
moves.sort()
k = len(moves)
mex = next((j for j in range(k) if moves[j] != j), k)
res.append(mex)
return res
# Eric M. Schmidt, Jul 20 2013, corrected Eric M. Schmidt, Apr 24 2019


CROSSREFS

Cf. A014586A014589.
Sequence in context: A069584 A199238 A181347 * A025658 A025673 A025688
Adjacent sequences: A014584 A014585 A014586 * A014588 A014589 A014590


KEYWORD

nonn


AUTHOR

Achim Flammenkamp


STATUS

approved



