0,4

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.

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.

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

Adjacent sequences: A131466 A131467 A131468 this_sequence A131470 A131471 A131472

Sequence in context: A139169 A076742 A036465 this_sequence A073078 A034799 A008985

nonn

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