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

1,2

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

Links

Table of n, a(n) for n=1..14.

Michael S. Branicky, RATS Sequence Cycles.

Tanya Khovanova, Destinies of Numbers. [From Tanya Khovanova, Aug 10 2009]

Example

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.

Crossrefs

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

Sequence in context: A058145 A218915 A258064 * A192245 A338645 A242558

Adjacent sequences: A161587 A161588 A161589 * A161591 A161592 A161593

Keyword

nonn,base,more

Author

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

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

Status

approved