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

2,2

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.

Links

Table of n, a(n) for n=2..70.

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

Example

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.

Crossrefs

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

Sequence in context: A055674 A210612 A266275 * A268864 A329956 A242703

Adjacent sequences: A288533 A288534 A288535 * A288537 A288538 A288539

Keyword

nonn,base

Author

Andrey Zabolotskiy, Jun 11 2017

Status

approved