A072140 The period length of the 'Reverse and Subtract' trajectory of n is greater than 1.

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

Offset: 1

Author

Klaus Brockhaus, Jun 24 2002

Keywords

• base
• nonn

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 analog of A023108, which uses 'Reverse and Add'. - A072141, A072142, A072143 give the numbers which generate periods of length 2, 14, 22 respectively.

Examples

			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.
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023108, A072137, A072141, A072142, A072143.

Programs

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.
-- Reinhard Zumkeller, Oct 24 2010