A131469 Grundy numbers of one pile short global nim.

0, 1, 1, 2, 3, 3, 2, 4, 5, 5, 6, 7, 7, 6, 4, 8, 9, 9, 8, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 14, 18, 19, 16, 17, 18, 20, 10, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 24, 26, 27, 27, 28

Offset

0,4

Comments

The game short global nim is identical to nim except that the last move cannot be repeated. (For example, if 2 stones were taken last turn, any number except 2 may be taken this turn.) The i-th term is the Grundy number of a pile of size i.

References

R. K. Guy and R. J. Nowakowski, Unsolved Problems in Combinatorial Games, More Games of No Chance, MSRI Publications, Volume 42, 2002, pp. 457-473, problem 22.

Links

Table of n, a(n) for n=0..53.

Urban Larsson, Simon Rubinstein-Salzedo, Aaron N. Siegel, Memgames, arXiv:1912.10517 [math.CO], 2019.

Maple

mex := proc (list) local testn; testn := 0; while evalb(`in`(testn, list)) do testn := testn+1 end do; testn end proc
nextmoves := proc (move) local i, j, k, l, list1, list2, list3, list4, list5, list6; i := move[1]; j := move[2]; k := move[3]; list1 := `minus`({seq([n, j, i-n], n = 0 .. i-1)}, {[i-k, j, k]}); list2 := `minus`({seq([i, n, j-n], n = 0 .. j-1)}, {[i, j-k, k]}); convert(`union`(list1, list2), list) end proc
sgnimgrundy := proc (move) local nmoves, i, j, k; option remember; nmoves := nextmoves(move); i := move[1]; j := move[2]; k := move[3]; if i = 0 and j = 0 then 0 elif i = 0 and j = 1 and k = 1 then 0 elif i = 1 and j = 0 and k = 1 then 0 elif i = 1 and j = 1 and k = 1 then 0 else mex({seq(apply(sgnimgrundy, nmoves[i]), i = 1 .. nops(nmoves))}) end if end proc

Crossrefs

Sequence in context: A265339 A372048 A182865 * A309076 A393434 A379777

Adjacent sequences: A131466 A131467 A131468 * A131470 A131471 A131472

Keyword

nonn

Author

Mark Schlatter (mschlat(AT)centenary.edu) and Jeffery James (jjames(AT)centenary.edu), Jul 26 2007

Status

approved