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Search: id:A067018
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| A067018 |
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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 (nim-sum a(i)+a(n-i)), where mex means smallest nonnegative missing number. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Nim-sum is addition in base 2 without carry (XOR the binary expansions).
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, E27.
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EXAMPLE
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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
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CROSSREFS
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Cf. A067016, A067017.
Sequence in context: A154960 A143543 A067017 this_sequence A100802 A022960 A023446
Adjacent sequences: A067015 A067016 A067017 this_sequence A067019 A067020 A067021
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 17 2002
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EXTENSIONS
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More terms from John W. Layman (layman(AT)math.vt.edu), Feb 20 2002
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