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

Author

Nathan Fox, May 03 2014

Keywords

• nonn

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

• 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.

Crossrefs

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

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.