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A046459 Dudeney numbers: integers equal to the sum of the digits of their cubes. 14

%I #53 Jan 04 2024 03:22:41

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

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

%C 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

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

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

%D Italo Ghersi, Matematica dilettevole e curiosa, p. 115, Hoepli, Milano, 1967. [From _Vincenzo Librandi_, Jan 02 2009]

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

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

%H H. E. Dudeney, <a href="https://archive.org/details/536PuzzlesCuriousProblems">536 Puzzles & Curious Problems</a>

%H The Mathematics Teacher, <a href="https://doi.org/10.5951/mathteacher.112.2.0120">October 2018 Calendar and Solutions</a>, Volume 112, Number 2, October 2018, pages 120 and 122.

%H ProofWiki, <a href="https://proofwiki.org/wiki/Sequence_of_Dudeney_Numbers">Sequence of Dudeney Numbers</a>

%H Bernard Schott and Norbert Verdier, <a href="http://www.les-mathematiques.net/phorum/read.php?17,493170">QDL 19: Quels beaux cubes!</a> (French mathematical forum les-mathematiques.net)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>

%e a(3) = 8 because 8^3 = 512 and 5 + 1 + 2 = 8.

%e a(7) = 27 because 27^3 = 19683 and 1 + 9 + 6 + 8 + 3 = 27.

%t Select[Range[0,30],#==Total[IntegerDigits[#^3]]&] (* _Harvey P. Dale_, Dec 21 2014 *)

%o (Magma) [n: n in [0..100] | &+Intseq(n^3) eq n ]; // _Vincenzo Librandi_, Sep 16 2015

%o (Python) a = [n for n in range(100) if sum(map(int, str(n ** 3))) == n] # _David Radcliffe_, Aug 18 2022

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

%Y Cf. A152147.

%K base,fini,full,nonn

%O 1,3

%A _Patrick De Geest_, Aug 15 1998

%E Offset corrected by _Arkadiusz Wesolowski_, Aug 09 2013

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)