|
%I #17 Apr 07 2024 17:42:57
%S 4,8,11,15,21,29,40,55,76,105,145,200,276,381,526,726,1002,1383,1909,
%T 2635,3637,5020,6929,9564,13201,18221,25150,34714,47915,66136,91286,
%U 126000,173915,240051,331337,457337,631252,871303,1202640,1659977,2291229,3162532,4365172
%N Smallest losing position after your opponent has taken k stones in a variation of "Fibonacci Nim".
%C In Fibonacci Nim, the first player takes any number of stones (except all) and then each player takes no more than twice the number taken in the previous move. This sequence concerns the game where 2 is replaced by 3.
%D R. K. Guy, Fair Game: How to play impartial combinatorial games, COMAP's Mathematical Exploration Series, 1989; see p. 22.
%e If your opponent has just removed 1 or 2 stones from the pile leaving you with 8, then you lose. Any fewer stones after your opponent has taken 2 will be a win for you.
%o (Python)
%o MAXTERM=10**9
%o cache, oldk = [MAXTERM], 1
%o for nleft in range(1,MAXTERM+1):
%o for k in range(1,nleft+1):
%o if k<cache[nleft-k]:
%o mk=(k+2)//3
%o break
%o cache.append(mk)
%o if mk>oldk:
%o print(nleft)
%o oldk=mk
%o # _Bert Dobbelaere_, Apr 07 2024
%K nonn
%O 1,1
%A _Ken Levasseur_, Apr 22 2000
%E More terms from _Bert Dobbelaere_, Apr 07 2024
|
