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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-François 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 October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)