A161590 Initial value x of a RATS trajectory x->A036839(x) ending in a cycle unreachable by any smaller initial value.

1, 3, 9, 29, 69, 2079, 3999, 6999, 10677, 20169, 10049598, 20008989, 100014888, 100074268

Offset: 1

Author

J. H. Conway and Tanya Khovanova, Jun 14 2009, Jul 04 2009

Keywords

• nonn
• base
• more

Comments

This is one way of book-keeping of new "destinies" (the smallest element of the cycle that the trajectory ends up in).

The value 1 is a placeholder for all non-cyclic trajectories.

Next terms are respectively <= 10000122228, 20000666679, 2000001113379, 2000001113559, 9999999999999, 100000044444447. See Branicky link for further upper bounds. - Michael S. Branicky, Dec 30 2022

Examples

			The RATS (Reverse Add Then Sort) algorithm applied to 69 produces a sequence 69, 156, 78, 156, 78, ...
Its cycle {156, 78} appears not if the algorithm is started with any number in the range 0 to 68, so 69 is added to the sequence.
		

Links

• Michael S. Branicky, RATS Sequence Cycles.
• Tanya Khovanova, Destinies of Numbers. [From _Tanya Khovanova_, Aug 10 2009]

Crossrefs

Cf. A036839, A066710, A066711, A004000, A114611, A161592, A161593, A161596.

Extensions

10677, 20169 from Wouter Meeussen, Jul 04 2009

Definition rephrased by R. J. Mathar, Jul 08 2009

a(11)-a(14) from Michael S. Branicky, Dec 30 2022