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A072137
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Length of the preperiodic part of the 'Reverse and Subtract' trajectory of n.
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19
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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; internal format)
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OFFSET
| 0,11
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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 analogue of A033665, which uses 'Reverse and Add'.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 0..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 24 2010]
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EXAMPLE
| a(15) = 4 since 15 -> |15- 51| = 36 -> |36 - 63| = 27 -> |27 - 72| = 45 -> |45 - 54| = 9.
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MATHEMATICA
| a[n_] := (k = 0; FixedPoint[ (k++; Abs[# - FromDigits[ Reverse[ IntegerDigits[#] ] ] ]) &, n]; k - 1); Table[ a[n], {n, 0, 104}] (* From Jean-François Alcover, Dec 01 2011 *)
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PROG
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 24 2010: (Start)
(Other) Haskell
import Data.List (find, inits)
import Data.Maybe (fromJust)
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
a072137 = length . fst . spanCycle (abs . a056965)
-- eop. (End)
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CROSSREFS
| Cf. A033665, A070837, A070838, A072138, A072139, A072140, A072141, A072146, A072147.
Sequence in context: A126093 A065279 A151962 * A061569 A140835 A094965
Adjacent sequences: A072134 A072135 A072136 * A072138 A072139 A072140
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KEYWORD
| base,easy,nonn,nice
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 24 2002
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