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A014587 Nim function for Take-a-Factorial-Game (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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 0..10000

Achim Flammenkamp, Lange Perioden in Subtraktions-Spielen, 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[i-f] 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. A014586-A014589.

Sequence in context: A069584 A199238 A181347 * A025658 A025673 A025688

Adjacent sequences:  A014584 A014585 A014586 * A014588 A014589 A014590

KEYWORD

nonn

AUTHOR

Achim Flammenkamp

STATUS

approved

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Last modified October 20 10:00 EDT 2020. Contains 337900 sequences. (Running on oeis4.)