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A054736
Smallest losing position after your opponent has taken k stones in a variation of "Fibonacci Nim".
0
4, 8, 11, 15, 21, 29, 40, 55, 76, 105, 145, 200, 276, 381, 526, 726, 1002, 1383, 1909, 2635, 3637, 5020, 6929, 9564, 13201, 18221, 25150, 34714, 47915, 66136, 91286, 126000, 173915, 240051, 331337, 457337, 631252, 871303, 1202640, 1659977, 2291229, 3162532, 4365172
OFFSET
1,1
COMMENTS
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.
REFERENCES
R. K. Guy, Fair Game: How to play impartial combinatorial games, COMAP's Mathematical Exploration Series, 1989; see p. 22.
EXAMPLE
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.
PROG
(Python)
MAXTERM=10**9
cache, oldk = [MAXTERM], 1
for nleft in range(1, MAXTERM+1):
for k in range(1, nleft+1):
if k<cache[nleft-k]:
mk=(k+2)//3
break
cache.append(mk)
if mk>oldk:
print(nleft)
oldk=mk
# Bert Dobbelaere, Apr 07 2024
CROSSREFS
Sequence in context: A186926 A311056 A311057 * A024626 A311058 A311059
KEYWORD
nonn
AUTHOR
Ken Levasseur, Apr 22 2000
EXTENSIONS
More terms from Bert Dobbelaere, Apr 07 2024
STATUS
approved