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A110921 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. 1
1, 81, 1458, 1729 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
REFERENCES
Tricky Number, Science Illustrated, Jan/Feb 2009, page 80.
P. Odifreddi, Il museo dei numeri, Rizzoli, 2014, page 284.
LINKS
FORMULA
k such that A007953(k)*A004086(A007953(k)) = k. - Jonathan Vos Post, Dec 20 2008
EXAMPLE
n = 1729: s = 1 + 7 + 2 + 9 = 19, 19*91 = 1729.
MATHEMATICA
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 *)
PROG
#!/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; }
CROSSREFS
Sequence in context: A282646 A283542 A237771 * A236867 A203650 A284057
KEYWORD
nonn,base,fini,full
AUTHOR
Michael Vang (michael.vang(AT)gmail.com), Sep 22 2005
EXTENSIONS
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
STATUS
approved

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)