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A046695 Sprague-Grundy values for the game Couples-are-Forever (and for octal games .6, .601, .61, .611, .62, .621, .63, .631). 2
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 (list; graph; refs; listen; history; text; internal format)
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: A117398 A240852 A071486 * 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

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Last modified April 17 22:11 EDT 2015. Contains 256760 sequences.