A046695 - OEIS

%I #19 Mar 07 2020 21:21:48

%S 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,

%T 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,

%U 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

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

%H Allan C. Wechsler, <a href="/A046695/b046695.txt">Table of n, a(n) for n = 0..1000</a>

%H I. Caines et al., <a href="http://www.jstor.org/stable/2589561">Periods in taking and splitting games</a>, Amer. Math. Monthly, 106 (1999), 359-361.

%F a(n) = A071433(n-1). - Typo corrected by _Allan C. Wechsler_, Oct 24 2014

%o (Haskell)

%o nimSum 0 0 = 0

%o nimSum a 0 = a

%o nimSum 0 b = b

%o nimSum a b = 2*(nimSum (div a 2) (div b 2)) + (rem ((rem a 2) + (rem b 2)) 2)

%o mexp l = head (filter (\x -> (not (elem x l))) [0..])

%o a046695_list = map a046695 [0..]

%o a046695 0 = 0

%o a046695 1 = 0

%o a046695 n = mexp (a046695' n)

%o a046695' n = (map trymove [0..(div (n-1) 2)])

%o   where trymove k = nimSum (a046695_list !! k) (a046695_list !! (n-k-1))

%o -- _Allan C. Wechsler_, Nov 18 2014

%Y Cf. A071433.

%K nonn

%O 0,4

%A _N. J. A. Sloane_

%E Edited and extended by _Christian G. Bower_, Oct 22 2002