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A083379
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a(n) = the number of squares with at most n digits and first digit 1.
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0
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1, 2, 7, 20, 62, 193, 608, 1918, 6061, 19160, 60582, 191568, 605782, 1915640, 6057776, 19156359, 60577716, 191563545, 605777108, 1915635402
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Asymptotically, the probability that a square begins with 1 is (sqrt(2)-1)/(sqrt(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: A116408 A014983 A015518 * A000935 A035071 A055891
Adjacent sequences: A083376 A083377 A083378 * A083380 A083381 A083382
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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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