cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Original entry on oeis.org

0, 8, 2, 18, 2, 2, 2, 14, 2, 3, 2, 2, 2, 6
Offset: 1

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Author

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

Keywords

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

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

A161596 Numbers in cycles of RATS sequences.

Original entry on oeis.org

78, 111, 117, 156, 222, 288, 444, 888, 1223, 1677, 3489, 4444, 8888, 11119, 11127, 11667, 11999, 12333, 16777, 23388, 27888, 34589, 44556, 111177, 112333, 228888, 444455, 889999, 1111113, 1177777, 1788899, 2222244, 4446666, 4558889, 11144445, 13444447, 55556688
Offset: 1

Views

Author

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

Keywords

Comments

The set of all numbers in any cycle of RATS sequences, sorted into natural order.
This implies that for any value a(j) in this sequence, A036839(a(j)) is again member of the sequence.
See Branicky link for larger terms. - Michael S. Branicky, Dec 30 2022

Examples

			The numbers 111, 222, 444, 888, 1677, 3489, 12333 and 44556 are in the sequence because they are in the cycle shown in A066710. The numbers 117 and 288 are in the cycle demonstrated in A066711.
The numbers 4444, 8888, 16777, 34589, 112333, 444455, ..., 1112278888, 11999, 1119, 1223 are in the cycle started at A161590(4). The numbers 11127 and 23388 are in the cycle started at A161590(7).

Links

Crossrefs

Cf. A004000, A036839, A066711, A066710, A161590, A161592.

Extensions

Descriptive comment and examples added by R. J. Mathar, Jul 08 2009
a(20) and beyond from Michael S. Branicky, Dec 30 2022

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

Original entry on oeis.org

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

Views

Author

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

Keywords

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

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

A164338 Conway's creeper sequence.

Original entry on oeis.org

12334444, 55667777, 123334444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, 556666667777, 1233333334444, 5566666667777, 12333333334444, 55666666667777, 123333333334444
Offset: 1

Views

Author

David W. Wilson, Aug 13 2009

Keywords

Comments

Trajectory of 12334444 under the RATS function A036839.
John Conway calls this sequence "the creeper" and conjectures that the RATS trajectory of every n >= 1 eventually enters a cycle or the creeper. David Wilson confirms this conjecture for n <= 10^10.
Continues with the obvious digital pattern.
Since a(n+2) = a(n) except for an added digit, this sequence can be described as a quasi-cycle of period 2 with smallest element 12334444. This is how it is treated in related sequences such as A161590, A161592 and A161593.

Links

Crossrefs

Cf. A036839 (RATS function), A161590, A161592, A161593.
Cf. A114611, A114612.

Programs

  • Haskell
    a164338 n = a164338_list !! (n-1)
a164338_list = iterate a036839 12334444
-- Reinhard Zumkeller, Mar 14 2012

Formula

a(n+2) = 10 a(n) - 9996 (n odd)
a(n+2) = 10 a(n) - 9993 (n even)
a(n+4) = 11 a(n+2) - 10 a(n)
a(n + 1) = A036839(a(n)). [Reinhard Zumkeller, Mar 14 2012]
G.f.: x*(-55677770*x^3 - 12344440*x^2 + 55667777*x + 12334444)/(10*x^4 - 11*x^2 + 1). - Chai Wah Wu, Feb 08 2020
Showing 1-4 of 4 results.

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