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A110921
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Numbers n such that n = digit_sum(n)*R(digit_sum(n)) where digit_sum is the sum of digits and R is the digit reversal.
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1
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OFFSET
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1,2
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COMMENTS
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These are special Harshad (or Niven) numbers from A005349. They are mentioned in Simon Singh's book``The Simpsons and their Mathematical Secrets" , 2013, Bloomsbury, New York (in the German version ``Homers letzter Satz", Hanser, 2013, on p. 238). - Wolfdieter Lang, Feb 05 2014
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REFERENCES
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Tricky Number, Science Illustrated, Jan/Feb 2009, page 80.
P. Odifreddi, Il museo dei numeri, Rizzoli, 2014, page 284.
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LINKS
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Table of n, a(n) for n=1..4.
Wikipedia, Masahiko Fujiwara
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FORMULA
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k such that A007953(k)*A004086(A007953(k)) = k. - Jonathan Vos Post, Dec 20 2008
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EXAMPLE
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n = 1729: s = 1 + 7 + 2 + 9 = 19, 19*91 = 1729.
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MATHEMATICA
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dsrQ[n_]:=Module[{c=Total[IntegerDigits[n]]}, c IntegerReverse[c]==n]; Select[Range[2000], dsrQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 19 2020 *)
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PROG
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#!/usr/bin/perl -w use strict; my $i; my $j; for $i ( 1e0 .. 1e6 ) { my $sum = 0; my $rev = 0; for $j ( 1 .. length ( $i ) ) { $sum += substr ( $i, $j - 1, 1 ); } $rev = reverse $sum; print "$i " if $sum * $rev == $i; }
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CROSSREFS
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Cf. A004086, A007953.
Sequence in context: A282646 A283542 A237771 * A236867 A203650 A284057
Adjacent sequences: A110918 A110919 A110920 * A110922 A110923 A110924
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KEYWORD
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nonn,base,fini,full,changed
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AUTHOR
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Michael Vang (michael.vang(AT)gmail.com), Sep 22 2005
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EXTENSIONS
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Edited by N. J. A. Sloane, Jan 15 2009, at the suggestion of Klaus Brockhaus
Edited by Charles R Greathouse IV, Aug 03 2010
Title corrected by Wolfdieter Lang, Feb 05 2014
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STATUS
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approved
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