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Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = mex_i (a(i)+a(n-i)), where mex means smallest nonnegative missing number.
6

%I #9 Jul 13 2013 12:02:42

%S 1,4,3,2,0,0,0,0,0,5,1,1,1,1,1,6,2,2,0,0,0,0,0,5,1,1,1,1,1,6,2,2,0,0,

%T 0,0,0,5,1,1,1,1,1,6,2,2,0,0,0,0,0,5,1,1,1,1,1,6,2,2,0,0,0,0,0,5,1,1,

%U 1,1,1,6,2,2,0,0,0,0,0,5,1,1,1,1,1,6,2,2,0,0,0,0,0,5,1,1,1,1,1,6,2,2,0,0,0

%N Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = mex_i (a(i)+a(n-i)), where mex means smallest nonnegative missing number.

%D R. K. Guy, Unsolved Problems in Number Theory, E27.

%H Reinhard Zumkeller, <a href="/A067017/b067017.txt">Table of n, a(n) for n = 0..10000</a>

%o (Haskell)

%o import Data.List ((\\))

%o a067017 n = a067017_list !! n

%o a067017_list = [1,4,3,2] ++ f [2,3,4,1] where

%o f xs = mexi : f (mexi : xs) where

%o mexi = head $ [0..] \\ zipWith (+) xs (reverse xs)

%o -- _Reinhard Zumkeller_, May 05 2012

%Y Cf. A067016, A067018.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Feb 17 2002

%E More terms from _John W. Layman_, Feb 20 2002