A161592 Except for the first term the number in the sequence is the smallest number in a new cycle of a RATS sequence with a new destiny. The first term is the best analog of this for the "infinite cycle".

12334444, 111, 117, 1223, 78, 111177, 11127, 11144445, 11667, 1111113

Offset: 1

Author

J. H. Conway & Tanya Khovanova, Jun 14 2009

Keywords

• nonn
• base

Comments

"Destiny" means the smallest element of the cycle that the trajectory ends up in.

All seeds except those generating the cycles listed here produce an open non-cyclic family (thus without lowest element) but with a regular structure like 12334444, 55667777, 123334444, 556667777, 1233334444, 5566667777,..., and with an arbitrary start-up like 1, 2, 4, 8, 16, 77, 145, 668, 1345, 6677, 13444, 55778, 133345, 666677, 1333444, 5567777, 12333445, 66666677, 133333444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, ... Notice that here we fall into the regular regime starting with 1233334444 (four threes). The sequence gives 12-(two threes)-4444 as a representative with index 1. - Wouter Meeussen, Jul 26 2009

Links

• Tanya Khovanova, Destinies of Numbers - _Tanya Khovanova_, Aug 10 2009

Crossrefs

Cf. A004000, A036839, A066710, A066711, A161590.

Cf. A161593, A161596. - Tanya Khovanova, Aug 10 2009

Extensions

11667, 1111113 from Wouter Meeussen, Jul 04 2009