A124074 Consider the map that sends a number m to m - reverse(m) if that is nonnegative, otherwise to m + reverse(m). Sequence gives those numbers that reach a nonzero cycle under repeated application of this map.

119, 129, 169, 179, 188, 198, 200, 210, 218, 220, 228, 230, 240, 249, 250, 260, 268, 270, 278, 280, 287, 290, 297, 299, 300, 301, 310, 311, 317, 320, 321, 327, 330, 331, 340, 341, 348, 349, 350, 351, 360, 361, 367, 370, 371, 377, 380, 381, 386, 389, 390

Offset: 1

Author

Sébastien Dumortier, Nov 05 2006

Keywords

• base
• nonn

Comments

There are values of n that apparently grow without bounds under repeated application of this map beginning with 10598, 10698, 10798, 10898, 11588, 11688, 11788, 11888, 11999, ... - Ray Chandler, Oct 10 2017

Examples

			119 is a member because
119 + 911 = 1030 (since the difference is negative),
1030 - 0301 = 729 (since the difference is positive),
729 + 927 = 1656,
1656 + 6561 = 8217,
8217 - 7128 = 1089,
1089 + 9801 = 10890,
10890 - 09801 = 1089, so the terms are cyclic.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A001232 gives the nonzero fixed points of map.

Programs

Mathematica

With[{nn = 400}, Select[Range@ nn, LengthWhile[NestList[If[#1 < 0, #2, #1] & @@ {#1 - #2, #1 + #2} & @@ {#, IntegerReverse@ #} &, #1, #2], # > 0 &] == #2 + 1 & @@ {#, 2^Log2@ #} &]] (* Michael De Vlieger, Oct 10 2017 *)

Extensions

Definition clarified by Ray Chandler, Oct 10 2017