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A083380
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a(n) = the number of cubes with at most n digits and first digit 1.
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4
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| Asymptotically, the probability that a cube begins with 1 is (cuberoot(2)-1)/(cuberoot(10)-1).
A generalization to arbitrary powers is found in Huerlimann, 2003. By increasing power the probability distribution approaches Benford's law.
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REFERENCES
| W. Huerlimann, Integer powers and Benford's law, preprint, 2003, available at www.mathpreprints.com/math/Preprint/werner.huerlimann/20030603/1 or at www.geocities.com/hurlimann53 (list of publications)
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CROSSREFS
| Cf. A083377-A083380.
Sequence in context: A126017 A034468 A130668 * A018112 A192415 A201779
Adjacent sequences: A083377 A083378 A083379 * A083381 A083382 A083383
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KEYWORD
| base,easy,nonn
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AUTHOR
| Werner S. Huerlimann [H\"{u}rlimann] (whurlimann(AT)bluewin.ch), Jun 05 2003
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EXTENSIONS
| Edited by Don Reble (djr(AT)nk.ca), Nov 05 2005
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