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Search: id:A001232
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| A001232 |
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Numbers n such that 9*n = (n written backwards). |
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+0
10
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| 1089, 10989, 109989, 1099989, 10891089, 10999989, 108901089, 109999989, 1089001089, 1098910989, 1099999989, 10890001089, 10989010989, 10999999989, 108900001089, 108910891089, 109890010989, 109989109989, 109999999989
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Least n-digit number which is a factor of its reversal. Quotient is always 9. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 11 2004
Fixed points of the map which sends x to x - reverse(x) if that is positive, otherwise to x + reverse(x). - Sebastien DUMORTIER (sdumortier(AT)ac-limoges.fr), Nov 05 2006
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REFERENCES
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H. Camous, Jouer Avec Les maths, "Cardinaux Reversibles", Section I Problem 6 pp. 27;37-8 Les Editions D'Organisation Paris 1984.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, under #1093.
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FORMULA
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Theorem (David W. Wilson): Terms in this sequence have the form 99*m, where the decimal representation of m contains only 1's and 0's, is palindromic and contains no singleton 1's or 0's. Hence contains Fib([ k/2 ]-1) k-digit elements, k >= 4.
a(n)=11*(10^n -1)=11*A002283(n), for n>1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 11 2004
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EXAMPLE
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1089*9=9801.
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CROSSREFS
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Cf. A008918, A008919.
Sequence in context: A008919 A110843 A023093 this_sequence A039684 A023101 A031621
Adjacent sequences: A001229 A001230 A001231 this_sequence A001233 A001234 A001235
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KEYWORD
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base,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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Corrected and extended by David W. Wilson (davidwwilson(AT)comcast.net) Aug 15 1996, Dec 15 1997.
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