A242082 Nim sequence of game on n counters whose legal moves are removing some number of counters in A027941.

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

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