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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.

%I A124074 #19 Oct 11 2017 10:59:11
%S A124074 119,129,169,179,188,198,200,210,218,220,228,230,240,249,250,260,268,
%T A124074 270,278,280,287,290,297,299,300,301,310,311,317,320,321,327,330,331,
%U A124074 340,341,348,349,350,351,360,361,367,370,371,377,380,381,386,389,390
%N 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.
%C A124074 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
%H A124074 Ray Chandler, <a href="/A124074/b124074.txt">Table of n, a(n) for n = 1..5000</a>
%e A124074 119 is a member because
%e A124074 119 + 911 = 1030 (since the difference is negative),
%e A124074 1030 - 0301 = 729 (since the difference is positive),
%e A124074 729 + 927 = 1656,
%e A124074 1656 + 6561 = 8217,
%e A124074 8217 - 7128 = 1089,
%e A124074 1089 + 9801 = 10890,
%e A124074 10890 - 09801 = 1089, so the terms are cyclic.
%t A124074 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 *)
%Y A124074 Cf. A001232 gives the nonzero fixed points of map.
%K A124074 base,nonn
%O A124074 1,1
%A A124074 _Sébastien Dumortier_, Nov 05 2006
%E A124074 Definition clarified by _Ray Chandler_, Oct 10 2017