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

Author

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

Keywords

• more
• nonn
• base

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

Examples

			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.
		

Links

• 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.

Crossrefs

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

Cf. A161590, A161592, A161596.

Extensions

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

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