cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

Original entry on oeis.org

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

Views

Author

Patrick De Geest, Aug 15 1998

Keywords

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

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

A055570 Sum of digits of (a(n)^4) is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 26, 28, 36
Offset: 0

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(2) = 2 because 2^4 = 16 and 1+6 = 7>= 2

Crossrefs

Cf. A055565, A055575, A055568, A055569, A055571, A055572.

Programs

  • Mathematica
    Select[Range[0,50],Total[IntegerDigits[#^4]]>=#&] (* Harvey P. Dale, Jan 20 2020 *)

Extensions

Definition clarified by Harvey P. Dale, Jan 20 2020

A055571 Sum of digits of a(n)^5 is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 31, 33, 35, 36, 37, 38, 46
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(2) = 2 because 2^5 = 32 and 3+2 = 5>= 2

Crossrefs

Cf. A055566, A055576, A055568, A055569, A055570, A055572.

Programs

  • Mathematica
    Select[Range[0,50],Total[IntegerDigits[#^5]]>=#&] (* Harvey P. Dale, Jul 03 2021 *)

A055572 Sum of digits of a(n)^6 is greater than or equal to a(n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 39, 42, 44, 45, 46, 51, 52, 54, 64
Offset: 0

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			a(2) = 2 because 2^6 = 64 and 6+4 = 10>= 2

Crossrefs

Cf. A055567, A055577, A055568, A055569, A055570, A055571.

A055568 Numbers not greater than the sum of digits of their squares.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 17
Offset: 1

Views

Author

Henry Bottomley, May 26 2000

Keywords

Examples

			4 is a term because 4^2 = 16 and 1+6 = 7 >= 4.

Crossrefs

Cf. A004159, A055569, A055570, A055571, A055572.

A081030 a(n) = largest k such that (sum of digits of k^n) >= k.

Original entry on oeis.org

9, 17, 27, 36, 46, 64, 68, 74, 88, 117, 123, 138, 146, 154, 199, 204, 216, 232, 232, 242, 259, 256, 284, 323, 337, 344, 341, 357, 358, 396, 443, 393, 423, 465, 477, 484, 519, 521, 533, 518, 569, 597, 591, 626, 638, 682, 666, 667, 695, 712, 698, 739, 746, 784
Offset: 1

Views

Author

David W. Wilson, Mar 02 2003

Keywords

Examples

			a(2) = 17. We have 17^2 = 289 and 2+8+9 >= 17. No number > 17 has this property.

Crossrefs

Cf. A055568, A055569, A055570, A055571, A055572.

Programs

  • Mathematica
    (* the constant 20 may need to be higher for larger n *) Table[Select[Range[20*n], Total[IntegerDigits[#^n]] >= # &][[-1]], {n, 100}] (* T. D. Noe, Oct 21 2011 *)

Extensions

Definition corrected by Harvey P. Dale, Oct 21 2011
Showing 1-6 of 6 results.

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