A119451 Let S_n be the infinite sequence formed by starting with n and repeatedly reversing the digits and adding 16 to get the next term. Sequence gives number of steps for S_n to reach a cycle, or -1 if no cycle is ever reached.

721, 708, 686, 709, 714, 656, 724, 756, 662, 721, 708, 695, 664, 732, 728, 715, 720, 707, 685, 708, 713, 655, 723, 755, 661, 15, 707, 712, 699, 686, 700, 732, 710, 0, 729, 1, 694, 654, 731, 709, 687, 710, 715, 657, 725, 757, 663, 722, 709, 714, 701, 688, 702

Offset: 1

Author

Klaus Brockhaus, May 20 2006

Keywords

• nonn
• base

Comments

It is conjectured that S_n always reaches a cycle.

There is one cycle of length 54 (least component is 34, all components have at most four digits, cf. A119454), 19 different cycles of length 90 with 4-digit components (least components are 1027 + 2*k for k = 0, ..., 18, cf. A119455), 444 different cycles of length 450 with 6-digit components, 3 different cycles of length 810 with 6-digit components (least components are 101007, 101011, 101015), 19 different cycles of length 1890 with 6-digit components (least components are 100027 + 2*k for k = 0, ..., 18) and at least 19 different cycles of length 19890 with 8-digit components (least components are 10000027 + 2*k for k = 0, ..., 18).

Links

• N. J. A. Sloane and others, Sequences of RADD type, OEIS wiki.

Crossrefs

S_1 is given in A118533. Records: A119452; where records occur: A119453. Cycles of length 54 and 90 are in A119454 and A119455.