A161593 Lengths of new periods in the RATS sequence (0 replacing infinity).

0, 8, 2, 18, 2, 2, 2, 14, 2, 3, 2, 2, 2, 6

Offset

1,2

Comments

The values A114611(j) for those starting values j of the RATS mapping x->A036839(x) which end in cycles that cannot be reached starting from any smaller j.

Every integer > 1 appears in this sequence. - Andrey Zabolotskiy, Jun 11 2017

For other terms see Branicky link. - Michael S. Branicky, Dec 30 2022

Links

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

Michael S. Branicky, RATS Sequence Cycles.

Curtis Cooper, RATS.

Curtis Cooper and Robert E. Kennedy, Base 10 RATS Cycles and Arbitrarily Long Base 10 RATS Cycles, Applications of Fibonacci numbers, Vol. 8, Kluwer Acad. Publ., Dordrecht, 1999, pages 83-93.

Tanya Khovanova, Destinies of Numbers.

Example

a(1)=A114611(0). a(2)=A114611(j=3)=8 with a cycle of length 8 shown in A066710.
A114611(j=6)=8 does not contribute because the cycle is the same as reached from j=3.
a(3)=A114611(9)=2 with a new cycle of length 2 shown in A066711.
A114611(j=12)=8 does not contribute because the cycle is the same as reached from j=3.
A114611(j=15)=8 does not contribute because 15->66->123 is the cycle as reached from j=3.
A114611(j=18)=2 does not contribute because the cycle is the same as reached from j=9.
A114611(j=21)=8 does not contribute because 21->33->66 reaches the same cycle as started from j=3.
a(4)=A114611(j=29)=18.

Crossrefs

Cf. A004000, A036839, A066711, A066710, A288537.

Cf. A161590, A161592, A161596.

Sequence in context: A196170 A164587 A050096 * A008866 A180728 A308217

Adjacent sequences: A161590 A161591 A161592 * A161594 A161595 A161596

Keyword

more,nonn,base

Author

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

Extensions

Comment and examples added by R. J. Mathar, Jul 07 2009

a(9)-a(14) from Michael S. Branicky, Dec 30 2022

Status

approved