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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
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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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