cp's OEIS Frontend

A072137 Length of the preperiodic part of the 'Reverse and Subtract' trajectory of n.

%I A072137 #18 Jun 20 2018 01:32:24
%S A072137 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,
%T A072137 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,
%U A072137 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
%N A072137 Length of the preperiodic part of the 'Reverse and Subtract' trajectory of n.
%C A072137 'Reverse and Subtract' (cf. A070837, A070838) is defined by x -> |x - reverse(x)|, where reverse(x) is the digit reversal of x.
%C A072137 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.
%C A072137 The first n with period length 2 and a nontrivial periodic part is 1012 (cf. A072140).
%C A072137 This sequence is a weak analog of A033665, which uses 'Reverse and Add'.
%H A072137 R. Zumkeller, <a href="/A072137/b072137.txt">Table of n, a(n) for n = 0..10000</a>
%e A072137 a(15) = 4 since 15 -> |15- 51| = 36 -> |36 - 63| = 27 -> |27 - 72| = 45 -> |45 - 54| = 9.
%t A072137 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 *)
%o A072137 (Haskell)
%o A072137 import Data.List(inits, find); import Data.Maybe(fromJust)
%o A072137 a072137 :: Int -> Int
%o A072137 a072137 = length . fst . spanCycle (abs . a056965) where
%o A072137    spanCycle :: Eq a => (a -> a) -> a -> ([a],[a])
%o A072137    spanCycle f x = fromJust $ find (not . null . snd) $
%o A072137                               zipWith (span . (/=)) xs $ inits xs
%o A072137                    where xs = iterate f x
%o A072137 -- _Reinhard Zumkeller_, Oct 24 2010
%Y A072137 Cf. A033665, A070837, A070838, A072138, A072139, A072140, A072141, A072146, A072147.
%K A072137 base,easy,nonn,nice
%O A072137 0,11
%A A072137 _Klaus Brockhaus_, Jun 24 2002