A288536 The eventual period of the RATS sequence in base n starting from 1; 0 is for infinity.

1, 3, 2, 2, 8, 4, 3, 2, 0, 28, 90, 8, 72, 3, 4, 2, 64, 0, 18, 4, 18, 20, 396, 8, 160, 120, 18, 6, 28, 4, 5, 2, 210, 384, 240, 0, 648, 1242, 240, 4, 660, 18, 798, 380, 852, 1298, 1771, 8, 0, 160, 16, 372, 520, 1404, 1740, 6, 36, 2072, 1856, 380, 300, 215, 6, 2, 3384, 50, 2310, 3784, 2904

Offset: 2

Author

Andrey Zabolotskiy, Jun 11 2017

Keywords

• nonn
• base

Comments

Eventual period of 1 under the mapping x->A288535(n,x), or 0 if there is a divergence and thus no eventual period.

Column 1 of A288537.

In Thiel's terms, the zeroes a(10), a(19), and a(37) correspond to quasiperiodic divergent RATS sequences with quasiperiod 2, while a(50)=0 corresponds to a sequence with quasiperiod 3.

Examples

			In base 3, the RATS mapping acts as 1 -> 2 -> 4 (11 in base 3) -> 8 (22 in base 3) -> 13 (112 in base 3) -> 4, which has already been seen 3 steps ago, so a(3)=3.
		

Links

• S. Shattuck and C. Cooper, Divergent RATS sequences, Fibonacci Quart., 39 (2001), 101-106.
• J. Thiel, On RATS sequences in general bases, Integers, 14 (2014), #A50.
• Index entries for sequences related to RATS: Reverse, Add Then Sort

Crossrefs

Cf. A004000, A114611, A288535, A288537, A237671, A072137.