

A083379


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


3



1, 2, 7, 20, 62, 193, 608, 1918, 6061, 19160, 60582, 191568, 605782, 1915640, 6057776, 19156359, 60577716, 191563545, 605777108, 1915635402
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OFFSET

1,2


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 Hürlimann, 2004. As the power increases, the probability distribution approaches Benford's law.


LINKS

Table of n, a(n) for n=1..20.
W. Hürlimann, Integer powers and Benford's law, International Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 3946, 2004.
Index entries for sequences related to Benford's law


CROSSREFS

Cf. A083377, A083378, A083380.
Sequence in context: A116408 A015518 A014983 * A216246 A322202 A000935
Adjacent sequences: A083376 A083377 A083378 * A083380 A083381 A083382


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



