The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A329200 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A329200

The ghost iteration (A): add or subtract the number formed by absolute differences of digits (A040115), according to parity (even or odd).
(history; published version)

#26 by Andrew Howroyd at Sun Jan 15 18:38:42 EST 2023

STATUS

proposed

approved

#25 by Jon E. Schoenfield at Sun Jan 15 18:16:14 EST 2023

STATUS

editing

proposed

#24 by Jon E. Schoenfield at Sun Jan 15 18:16:10 EST 2023

COMMENTS

Sequence A040115 is most naturally extended to 0 (empty sum) for single -digit arguments, ; that's what we use here. This value is added to n if even, subtracted if odd.

STATUS

approved

editing

#23 by N. J. A. Sloane at Mon Jan 02 12:30:54 EST 2023

LINKS

E. Angelini, <a href="http://list.seqfan.eu/pipermailoldermail/seqfan/2019-November/">The ghost iteration</a>, SeqFan list, Nov 2019

Discussion

Mon Jan 02

12:30

OEIS Server: https://oeis.org/edit/global/2957

#22 by N. J. A. Sloane at Sun Nov 10 20:00:17 EST 2019

STATUS

proposed

approved

#21 by M. F. Hasler at Sun Nov 10 19:08:03 EST 2019

STATUS

editing

proposed

#20 by M. F. Hasler at Sun Nov 10 19:08:00 EST 2019

COMMENTS

Repdigit numbers are the fixed points. Others enter into Other starting values end in nontrivial loops under iterations of this map, like 11090 -> 10891 -> 12709 -> 11130 -> 11107 -> 11090 .etc. Table A329196 lists these cycles, A329197 their lengths.

A329198 gives the size of n's orbit, i.e., the length of the trajectory until the terminating cycle is covered.

CROSSREFS

Cf. A329196 (cycles), A329197 (lengths), A329198 (size of orbit of n).

STATUS

approved

editing

#19 by M. F. Hasler at Sun Nov 10 14:00:08 EST 2019

STATUS

editing

approved

#18 by M. F. Hasler at Sun Nov 10 13:58:13 EST 2019

COMMENTS

Repdigit numbers are the fixed points. Others enter into nontrivial loops under iterations of this map, like 11090 -> 10891 -> 12709 -> 11130 -> 11107 -> 11090 ...

STATUS

approved

editing

#17 by M. F. Hasler at Sun Nov 10 10:09:20 EST 2019

STATUS

editing

approved