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

Offset: 1

Author

Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003

Keywords

• base
• easy
• nonn

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.
• Index entries for sequences related to Benford's law

Crossrefs

Cf. A083377, A083378, A083379.

Extensions

Edited by Don Reble, Nov 05 2005