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.

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, 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, 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

Offset

0,9

Links

Table of n, a(n) for n=0..104.

Example

5 -> 10 -> 5 -> ..., so 5 is already in a cycle and a(5) = 0. 13 -> 44 -> 22 -> 11 -> 22 -> ..., so a(13) = 2.

Mathematica

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)

Crossrefs

Cf. A089381.

Sequence in context: A249142 A225099 A174806 * A218786 A218787 A325336

Adjacent sequences: A089602 A089603 A089604 * A089606 A089607 A089608

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Jan 01 2004

Extensions

More terms from John W. Layman and Robert G. Wilson v, Jan 05 2004

Status

approved