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A072137 Length of the preperiodic part of the 'Reverse and Subtract' trajectory of n. 20
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 1, 2, 6, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

'Reverse and Subtract' (cf. A070837, A070838) is defined by x -> |x - reverse(x)|, where reverse(x) is the digit reversal of x.

For every n the trajectory eventually becomes periodic, since 'Reverse and Subtract' does not increase the number of digits and so the set of available terms is finite. For small n the period length is 1, the periodic part consists of 0's, the last term of the preperiodic part is a palindrome.

The first n with period length 2 and a nontrivial periodic part is 1012 (cf. A072140).

This sequence is a weak analog of A033665, which uses 'Reverse and Add'.

LINKS

R. Zumkeller, Table of n, a(n) for n = 0..10000

EXAMPLE

a(15) = 4 since 15 -> |15- 51| = 36 -> |36 - 63| = 27 -> |27 - 72| = 45 -> |45 - 54| = 9.

MATHEMATICA

a[n_] := (k = 0; FixedPoint[ (k++; Abs[# - FromDigits[ Reverse[ IntegerDigits[#] ] ] ]) &, n]; k - 1); Table[ a[n], {n, 0, 104}] (* Jean-Fran├žois Alcover, Dec 01 2011 *)

PROG

(Haskell)

import Data.List(inits, find); import Data.Maybe(fromJust)

a072137 :: Int -> Int

a072137 = length . fst . spanCycle (abs . a056965) where

   spanCycle :: Eq a => (a -> a) -> a -> ([a], [a])

   spanCycle f x = fromJust $ find (not . null . snd) $

                              zipWith (span . (/=)) xs $ inits xs

                   where xs = iterate f x

-- Reinhard Zumkeller, Oct 24 2010

CROSSREFS

Cf. A033665, A070837, A070838, A072138, A072139, A072140, A072141, A072146, A072147.

Sequence in context: A126093 A065279 A151962 * A061569 A294523 A286651

Adjacent sequences:  A072134 A072135 A072136 * A072138 A072139 A072140

KEYWORD

base,easy,nonn,nice

AUTHOR

Klaus Brockhaus, Jun 24 2002

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)