A046043 Autobiographical numbers (or curious numbers): list of numbers m = x_0 x_1 x_2 ... x_{b-1} (written in base b) such that x_i is the number of "digits" in m that are equal to i, for all i=0,...,b-1.
1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000
Offset: 1
Examples
m = 1210 is written in base 4 (since it has 4 digits), and has one 0, two 1's, one 2 and zero 3's and m = "one two one zero".
References
- E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
- M. Gardner, Mathematical Circus, pp. 128; 135 Prob. 7 Alfred A. Knopf NY 1979.
- Tanya Khovanova, A Story of Storytelling Numbers, Math. Horizons, Sep 2009, 14-17.
Links
- Fred Gavin, Letters to the editor, Math. Mag 66 (4) (1993) p 276.
- Shyam Sunder Gupta, On Some Special Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 22, 527-565.
- Amy Harmon, Beyond 'Hidden Figures': Nurturing New Black and Latino Math Whizzes, New York Times, Feb 17, 2017.
- Tanya Khovanova, Autobiographical Numbers, arXiv:0803.0270 [math.CO], 2008.
- Chris Smith, #MegaFavNumbers Self-Descriptive Numbers (the beauty 6210001000), video (2020)
- K. Uhland, The Ten-Digit Number [Broken link?]
Programs
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Mathematica
isSelfDescribing[n_Integer] := (RotateRight[DigitCount[n]] == PadRight[IntegerDigits[n], 10]); Select[Range[10^10 - 1], isSelfDescribing] (* Martin Ettl, Oct 09 2012 *) (* Warning: This program causes Mathematica to crash! - David Callan, Feb 17 2017 *)
Extensions
Edited by N. J. A. Sloane, Aug 15 2019
Comments