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A242082
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Nim sequence of game on n counters whose legal moves are removing some number of counters in A027941.
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0
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0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0
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OFFSET
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0,5
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COMMENTS
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Aperiodic, ternary sequence.
Result of applying the map 0->01, 1->2 to A188432.
Let w(1)=01. For all i>1, let w(i)=w(i-1)w(i-1)w(i-2)...w(2)w(1)2 (as a concatenation of words). The limit of this process is this sequence.
Also the Nim sequence of game on n counters whose legal moves are removing either 1 counter or some number of counters in A089910.
a(n+2) = A159917(n), the infinite Fibonacci sequence on {0,1,2}. See also the standard form A270788 of A159917, explaining the formula below. - Michel Dekking, Dec 27 2016
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LINKS
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Table of n, a(n) for n=0..99.
N. Fox, Aperiodic Subtraction Games, Talk given at the Rutgers Experimental Mathematics Seminar, May 01 2014.
U. Larsson, N. Fox, An Aperiodic Subtraction Game of Nim-Dimension Two, Journal of Integer Sequences, 2015, Vol. 18, #15.7.4.
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FORMULA
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a(n)=0 if and only if n=0 or n is in A001950.
a(n)=1 if and only if a(n-1)=0, which happens if and only if n is in A026352.
a(n)=2 if and only if n is in A089910.
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CROSSREFS
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Cf. A027941, A001950, A000201, A026352, A089910.
Sequence in context: A122924 A133450 A029410 * A159917 A242081 A190487
Adjacent sequences: A242079 A242080 A242081 * A242083 A242084 A242085
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KEYWORD
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nonn
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AUTHOR
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Nathan Fox, May 03 2014
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STATUS
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approved
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