%I A089605
%S A089605 0,0,0,0,1,0,0,0,2,0,0,0,1,2,0,1,3,3,0,1,1,1,0,1,2,1,3,1,1,1,2,2,4,0,4,
%T A089605 3,1,1,2,2,2,1,2,1,1,1,2,1,3,3,2,1,4,3,2,0,2,2,2,1,3,1,3,1,5,1,0,3,5,2,
%U A089605 4,3,2,1,2,2,3,0,3,4,3,1,2,1,3,3,2,2,2,4,2,1,3,2,2,1,4,4,4,0,3,0,2,2,5
%N A089605 Let P(m) = m/2 if m is even, m + rev(m) if m is odd, where rev(m) is 
               m's base 10 representation reversed. It is conjectured that any number 
               k eventually cycles when P is repeatedly applied to it. Sequence 
               gives number of steps before the cycle is reached.
%e A089605 5 -> 10 -> 5 -> ..., so 5 is already in a cycle and a(5) = 0. 13 -> 44 
               -> 22 -> 11 -> 22 -> ..., so a(13) = 2.
%t A089605 Step[n_] := If[ EvenQ[n], n/2, n + FromDigits[ Reverse[ IntegerDigits[n]]]]; 
               cPalHash = 1013; clearArray = Array[{} &, cPalHash]; InsertCheck[n_, 
               a_] := Module[{i = Mod[n, cPalHash] + 1}, a[[i]] = Append[a[[i]], 
               n]]; SetAttributes[ InsertCheck, HoldRest]; CheckArray[n_, a_] := 
               MemberQ[ a[[Mod[n, cPalHash] + 1]], n]; SetAttributes[ CheckArray, 
               HoldRest]; PalListHelper[n_, cTries_] := Module[{ch = clearArray}, 
               NestWhileList[ (InsertCheck[ #, ch]; Step[ # ]) &, n, Not[ CheckArray[ 
               #, ch]] &, 1, cTries]]; PalList[n_, cTries_] := Module[{lst, nRemoved, 
               loop}, lst = PalListHelper[n, cTries]; nRemoved = First[ First[ Position[lst, 
               lst[[ -1]]]]]; loop = Drop[ Take[lst, {nRemoved, -1}], -1]; Append[ 
               Take[lst, {1, nRemoved - 1}], loop]]; Table[ Length[ PalList[n, 1013]] 
               - 1, {n, 0, 104}] (from Darrell Plank (jar_czar(AT)msn.com), Dec 
               28 2003)
%Y A089605 Cf. A089381.
%Y A089605 Sequence in context: A079126 A025891 A120630 this_sequence A060016 A117408 
               A079100
%Y A089605 Adjacent sequences: A089602 A089603 A089604 this_sequence A089606 A089607 
               A089608
%K A089605 nonn,base,easy
%O A089605 0,9
%A A089605 N. J. A. Sloane (njas(AT)research.att.com), Jan 01 2004
%E A089605 More terms from John W. Layman (layman(AT)math.vt.edu) and Robert G. 
               Wilson v (rgwv(AT)rgwv.com), Jan 05 2004