A083380 - OEIS

A083380

a(n) is the number of cubes with at most n digits and first digit 1.

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

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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

Table of n, a(n) for n=1..30.

W. Hürlimann, Integer powers and Benford's law, International Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 39-46, 2004.

Index entries for sequences related to Benford's law

CROSSREFS

Cf. A083377, A083378, A083379.

Sequence in context: A283075 A130668 A358912 * A018112 A274489 A192415

Adjacent sequences: A083377 A083378 A083379 * A083381 A083382 A083383

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