

A046695


SpragueGrundy values for the game CouplesareForever (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
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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), 359361.


FORMULA

a(n) = A071433(n1).  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 (n1) 2)])
where trymove k = nimSum (a046695_list !! k) (a046695_list !! (nk1))
 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



