cp's OEIS Frontend

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.

%I A089605 #12 Aug 12 2025 02:02:16
%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,
%T A089605 4,3,1,1,2,2,2,1,2,1,1,1,2,1,3,3,2,1,4,3,2,0,2,2,2,1,3,1,3,1,5,1,0,3,
%U A089605 5,2,4,3,2,1,2,2,3,0,3,4,3,1,2,1,3,3,2,2,2,4,2,1,3,2,2,1,4,4,4,0,3,0,2,2,5
%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.
%e A089605 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}] (* Darrell Plank (jar_czar(AT)msn.com), Dec 28 2003 *)
%Y A089605 Cf. A089381.
%K A089605 nonn,base,easy
%O A089605 0,9
%A A089605 _N. J. A. Sloane_, Jan 01 2004
%E A089605 More terms from _John W. Layman_ and _Robert G. Wilson v_, Jan 05 2004