A046459 Dudeney numbers: integers equal to the sum of the digits of their cubes.

0, 1, 8, 17, 18, 26, 27

Offset

1,3

Comments

This sequence was first found by the French mathematician Claude (Séraphin) Moret-Blanc in 1879. See Le Lionnais page 27 for the last term of this sequence: 27. - Bernard Schott, Dec 07 2012

The name "Dudeney numbers" appears in the October 2018 issue of Mathematics Teacher (see link). - N. J. A. Sloane, Oct 10 2018

References

H. E. Dudeney, 536 Puzzles & Curious Problems, reprinted by Souvenir Press, London, 1968, p. 36, #120.

Italo Ghersi, Matematica dilettevole e curiosa, p. 115, Hoepli, Milano, 1967. [From Vincenzo Librandi, Jan 02 2009]

F. Le Lionnais, Les nombres remarquables, Hermann, 1983.

J. Roberts, Lure of the Integers, The Mathematical Association of America, 1992, p. 172.

Links

Table of n, a(n) for n=1..7.

H. E. Dudeney, 536 Puzzles & Curious Problems

The Mathematics Teacher, October 2018 Calendar and Solutions, Volume 112, Number 2, October 2018, pages 120 and 122.

ProofWiki, Sequence of Dudeney Numbers

Bernard Schott and Norbert Verdier, QDL 19: Quels beaux cubes! (French mathematical forum les-mathematiques.net)

Eric Weisstein's World of Mathematics, Cubic Number

Example

a(3) = 8 because 8^3 = 512 and 5 + 1 + 2 = 8.
a(7) = 27 because 27^3 = 19683 and 1 + 9 + 6 + 8 + 3 = 27.

Mathematica

Select[Range[0, 30], #==Total[IntegerDigits[#^3]]&] (* Harvey P. Dale, Dec 21 2014 *)

Prog

(Magma) [n: n in [0..100] | &+Intseq(n^3) eq n ]; // Vincenzo Librandi, Sep 16 2015
(Python) a = [n for n in range(100) if sum(map(int, str(n ** 3))) == n] # David Radcliffe, Aug 18 2022

Crossrefs

Cf. A004164, A055569, A055575, A055576, A055577.

Cf. A152147.

Sequence in context: A066554 A302976 A244537 * A274770 A075485 A217433

Adjacent sequences: A046456 A046457 A046458 * A046460 A046461 A046462

Keyword

base,fini,full,nonn

Author

Patrick De Geest, Aug 15 1998

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 09 2013

Status

approved