A083379 a(n) = the number of squares with at most n digits and first digit 1.

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

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

Robert Israel, Table of n, a(n) for n = 1..1999

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

Maple

ListTools:-PartialSums([seq(floor(sqrt(2*10^n))-ceil(sqrt(10^n))+1, n=0..20)]); # Robert Israel, Feb 15 2021

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