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
Keywords
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.
Crossrefs
Cf. A071433.
Programs
-
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
Formula
a(n) = A071433(n-1). - Typo corrected by Allan C. Wechsler, Oct 24 2014
Extensions
Edited and extended by Christian G. Bower, Oct 22 2002