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A242082 Nim sequence of game on n counters whose legal moves are removing some number of counters in A027941. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

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.

FORMULA

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.

CROSSREFS

Cf. A027941, A001950, A000201, A026352, A089910.

Sequence in context: A122924 A133450 A029410 * A159917 A242081 A190487

Adjacent sequences:  A242079 A242080 A242081 * A242083 A242084 A242085

KEYWORD

nonn

AUTHOR

Nathan Fox, May 03 2014

STATUS

approved

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Last modified February 24 02:48 EST 2020. Contains 332195 sequences. (Running on oeis4.)