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A001232 Numbers n such that 9*n = (n written backwards), n > 0. 15
1089, 10989, 109989, 1099989, 10891089, 10999989, 108901089, 109999989, 1089001089, 1098910989, 1099999989, 10890001089, 10989010989, 10999999989, 108900001089, 108910891089, 109890010989, 109989109989, 109999999989, 1089000001089, 1089109891089 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence contains the least n-digit non-palindromic number which is a factor of its reversal. Quotient is always 9. - Lekraj Beedassy, Jun 11 2004. (But it contains many other numbers as well. - N. J. A. Sloane, Jul 02 2013)

Nonzero fixed points of the map which sends x to x - reverse(x) if that is nonnegative, otherwise to x + reverse(x). - Sébastien Dumortier, Nov 05 2006. (Clarified comment, see A124074. - Ray Chandler, Oct 11 2017)

Numbers n such that reversal(n)=reversal(n+reversal(n)). Also numbers n such that reversal(n)=reversal(10*n-reversal(n)). - Farideh Firoozbakht, Jun 11 2010

REFERENCES

H. Camous, Jouer Avec Les Maths, "Cardinaux Réversibles", Section I, Problem 6, pp. 27, 37-38; Les Editions d'Organisation, Paris, 1984.

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, under #1093.

LINKS

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

L. H. Kendrick, Young Graphs: 1089 et al., J. Int. Seq. 18 (2015) 15.9.7.

N. J. A. Sloane, 2178 And All That, Fib. Quart., 52 (2014), 99-120.

FORMULA

Theorem: 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(floor(k/2)-1) k-digit terms, k >= 4. - David W. Wilson, Dec 15 1997

a(A094707(n)) = 11*(10^n -1) = 11*A002283(n) = 99*A002275(n), for n>1. - Lekraj Beedassy, Jun 11 2004. (Restored from history and corrected. - Ray Chandler, Oct 11 2017)

EXAMPLE

1089*9 = 9801.

MATHEMATICA

Rest@Select[FromDigits /@ Tuples[{0, 99}, 11], IntegerDigits[9*#] == Reverse@IntegerDigits[#] &] (* Arkadiusz Wesolowski, Aug 14 2012 *)

okQ[t_]:=t==Reverse[t]&&First[t]!=0&&Min[Length/@Split[t]]>1; 99#&/@Flatten[Table[FromDigits/@Select[Tuples[{0, 1}, n], okQ], {n, 20}]] (* Harvey P. Dale, Jul 03 2013 *)

PROG

(PARI) isok(n) = 9*n == eval(concat(Vecrev(Str(n)))); \\ Michel Marcus, Feb 21 2015

CROSSREFS

Cf. A008918, A008919, A193434, A222814, A222815, A031877, A124074.

Cf. A002275, A002283, A094707.

Sequence in context: A319570 A319482 A023093 * A039684 A230066 A274755

Adjacent sequences:  A001229 A001230 A001231 * A001233 A001234 A001235

KEYWORD

base,nonn,nice

AUTHOR

N. J. A. Sloane and Simon Plouffe

EXTENSIONS

Corrected and extended by David W. Wilson, Aug 15 1996, Dec 15 1997

a(20)-a(21) from Arkadiusz Wesolowski, Aug 14 2012

STATUS

approved

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Last modified November 14 06:14 EST 2018. Contains 317162 sequences. (Running on oeis4.)