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A083380 a(n) is the number of cubes with at most n digits and first digit 1. 3
1, 1, 2, 5, 11, 23, 49, 105, 225, 485, 1045, 2252, 4852, 10452, 22517, 48510, 104508, 225153, 485075, 1045058, 2251505, 4850716, 10450546, 22515012, 48507117, 104505409, 225150073, 485071123, 1045054049, 2251500692 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Asymptotically, the probability that a cube begins with 1 is (2^(1/3) - 1)/(10^(1/3) - 1).
A generalization to arbitrary powers is found in Hürlimann, 2004. As the power increases, the probability distribution approaches Benford's law.
LINKS
W. Hürlimann, Integer powers and Benford's law, International Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 39-46, 2004.
CROSSREFS
Sequence in context: A283075 A130668 A358912 * A018112 A274489 A192415
KEYWORD
base,easy,nonn
AUTHOR
Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003
EXTENSIONS
Edited by Don Reble, Nov 05 2005
STATUS
approved

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)