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

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

Offset: 1

Author

Patrick De Geest, Aug 15 1998

Keywords

• base
• fini
• full
• nonn

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

Examples

			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.
		

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.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 96.

Links

• 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.

Crossrefs

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

Cf. A152147.

Programs

Magma

[n: n in [0..100] | &+Intseq(n^3) eq n ]; // Vincenzo Librandi, Sep 16 2015

Mathematica

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

PARI

isok(k)=sumdigits(k^3)==k \\ Patrick De Geest, Dec 10 2024

Python

a = [n for n in range(100) if sum(map(int, str(n ** 3))) == n] # David Radcliffe, Aug 18 2022

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 09 2013