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

1,1

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A001232 gives the nonzero fixed points of map.

Sequence in context: A049048 A328973 A133626 * A231372 A103154 A039557

Adjacent sequences: A124071 A124072 A124073 * A124075 A124076 A124077

Keyword

base,nonn

Author

Sébastien Dumortier, Nov 05 2006

Extensions

Definition clarified by Ray Chandler, Oct 10 2017

Status

approved