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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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FORMULA
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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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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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STATUS
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approved
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