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.

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, 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, 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

Offset: 0

Author

N. J. A. Sloane, Feb 17 2002

Keywords

• nonn
• easy

Comments

Nim-sum is addition in base 2 without carry (XOR the binary expansions).

Examples

			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
		

References

• R. K. Guy, Unsolved Problems in Number Theory, E27.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A067016, A067017.

Programs

Haskell

import Data.Bits (xor)
import Data.List ((\\))
a067018 n = a067018_list !! n
a067018_list =  [1,4,3,2] ++ f [2,3,4,1] where
  f xs = mexi : f (mexi : xs) where
    mexi = head $ [0..] \\ zipWith xor xs (reverse xs) :: Integer
-- Reinhard Zumkeller, May 05 2012

Extensions

More terms from John W. Layman, Feb 20 2002