cp's OEIS Frontend

A067018 Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = mex_i (nim-sum a(i)+a(n-i)), where mex means smallest nonnegative missing number.

%I A067018 #10 Jul 13 2013 12:02:42
%S A067018 1,4,3,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,
%T A067018 0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,
%U A067018 0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0,2,0
%N A067018 Start with a(0)=1, a(1)=4, a(2)=3, a(3)=2; for n>=3, a(n+1) = mex_i (nim-sum a(i)+a(n-i)), where mex means smallest nonnegative missing number.
%C A067018 Nim-sum is addition in base 2 without carry (XOR the binary expansions).
%D A067018 R. K. Guy, Unsolved Problems in Number Theory, E27.
%H A067018 Reinhard Zumkeller, <a href="/A067018/b067018.txt">Table of n, a(n) for n = 0..10000</a>
%e A067018 a(5) = mex{1 xor 0, 4 xor 2, 3 xor 3, etc. (duplicates)} = mex{1 xor 0, 100 xor 10, 11 xor 11} (in base 2) = mex{1, 6, 0} = 2
%o A067018 (Haskell)
%o A067018 import Data.Bits (xor)
%o A067018 import Data.List ((\\))
%o A067018 a067018 n = a067018_list !! n
%o A067018 a067018_list =  [1,4,3,2] ++ f [2,3,4,1] where
%o A067018   f xs = mexi : f (mexi : xs) where
%o A067018     mexi = head $ [0..] \\ zipWith xor xs (reverse xs) :: Integer
%o A067018 -- _Reinhard Zumkeller_, May 05 2012
%Y A067018 Cf. A067016, A067017.
%K A067018 nonn,easy
%O A067018 0,2
%A A067018 _N. J. A. Sloane_, Feb 17 2002
%E A067018 More terms from _John W. Layman_, Feb 20 2002