

A072140


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


9



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
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OFFSET

1,1


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.


LINKS

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


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.


PROG

Contribution from Reinhard Zumkeller, 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)


CROSSREFS

Cf. A023108, A072137, A072141, A072142, A072143.
Sequence in context: A094946 A158877 A159774 * A080467 A023058 A223077
Adjacent sequences: A072137 A072138 A072139 * A072141 A072142 A072143


KEYWORD

base,nonn


AUTHOR

Klaus Brockhaus, Jun 24 2002


STATUS

approved



