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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 (list; graph; refs; listen; history; text; internal format)
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. 39-46, 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

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Last modified February 20 15:52 EST 2020. Contains 332078 sequences. (Running on oeis4.)