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, 81, 1458, 1729

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

Table of n, a(n) for n=1..4.

Wikipedia, Masahiko Fujiwara

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

(Perl)
#!/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

Cf. A004086, A007953.

Sequence in context: A282646 A283542 A237771 * A236867 A203650 A284057

Adjacent sequences: A110918 A110919 A110920 * A110922 A110923 A110924

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