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A072140
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The period length of the 'Reverse and Subtract' trajectory of n is greater than 1.
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8
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1012, 1023, 1034, 1045, 1067, 1078, 1089, 1100, 1122, 1133, 1144, 1155, 1177, 1188, 1199, 1210, 1232, 1243, 1254, 1265, 1287, 1298, 1320, 1342, 1353, 1364, 1375, 1397, 1408, 1430, 1452, 1463, 1474, 1485, 1507, 1518, 1540, 1562, 1573, 1584, 1595, 1606
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 'Reverse and Subtract' (cf. A072137) is defined by x -> |x - reverse(x)|. There is no number k > 0 such that |k - reverse(k)| = k, so 0 is the only period with length 1. Consequently this sequence consists of the numbers n such that repeated application of 'Reverse and Subtract' does not lead to a palindrome. It is an analogue of A023108, which uses 'Reverse and Add'. - A072141, A072142, A072143 give the numbers which generate periods of length 2, 14, 22 respectively.
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EXAMPLE
| 1012 -> |1012 - 2101| = 1089 -> |1089 - 9801| = 8712 -> |8712 - 2178| = 6534 -> |6534 - 4356| = 2178 -> |2178 - 8712| = 6534; the period of the trajectory is 6534, 2178 and a palindrome is never reached.
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PROG
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 24 2010: (Start)
(Other) Haskell:
import Data.List (find, findIndices, 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
a072140_list = findIndices (> 1) $
.............. map (length . snd . spanCycle (abs . a056965)) [0..]
-- eop. (End)
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CROSSREFS
| Cf. A023108, A072137, A072141, A072142, A072143.
Sequence in context: A094946 A158877 A159774 * A080467 A023058 A206191
Adjacent sequences: A072137 A072138 A072139 * A072141 A072142 A072143
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KEYWORD
| base,nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 24 2002
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