A046695 Sprague-Grundy values for the game Couples-are-Forever (and for octal games .6, .601, .61, .611, .62, .621, .63, .631).

0, 0, 1, 2, 0, 1, 2, 3, 1, 2, 3, 4, 0, 3, 4, 2, 1, 3, 2, 1, 0, 2, 1, 4, 5, 1, 4, 5, 1, 2, 0, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 1, 0, 2, 8, 4, 5, 3, 4, 5, 6, 2, 5, 1, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 0, 2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 2, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 4, 2, 3, 0, 2, 3, 4

Offset

0,4

Links

Allan C. Wechsler, Table of n, a(n) for n = 0..1000

I. Caines et al., Periods in taking and splitting games, Amer. Math. Monthly, 106 (1999), 359-361.

Formula

a(n) = A071433(n-1). - Typo corrected by Allan C. Wechsler, Oct 24 2014

Prog

(Haskell)
nimSum 0 0 = 0
nimSum a 0 = a
nimSum 0 b = b
nimSum a b = 2*(nimSum (div a 2) (div b 2)) + (rem ((rem a 2) + (rem b 2)) 2)
mexp l = head (filter (\x -> (not (elem x l))) [0..])
a046695_list = map a046695 [0..]
a046695 0 = 0
a046695 1 = 0
a046695 n = mexp (a046695' n)
a046695' n = (map trymove [0..(div (n-1) 2)])
  where trymove k = nimSum (a046695_list !! k) (a046695_list !! (n-k-1))
-- Allan C. Wechsler, Nov 18 2014

Crossrefs

Cf. A071433.

Sequence in context: A309816 A071486 A336684 * A071433 A110657 A071512

Adjacent sequences: A046692 A046693 A046694 * A046696 A046697 A046698

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited and extended by Christian G. Bower, Oct 22 2002

Status

approved