A054736 Smallest losing position after your opponent has taken k stones in a variation of "Fibonacci Nim".

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.

Links

Table of n, a(n) for n=1..43.

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

Adjacent sequences: A054733 A054734 A054735 * A054737 A054738 A054739

Keyword

nonn

Author

Ken Levasseur, Apr 22 2000

Extensions

More terms from Bert Dobbelaere, Apr 07 2024

Status

approved