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A083379 a(n) = the number of squares with at most n digits and first digit 1. 4

%I #22 Feb 15 2021 22:40:49

%S 1,2,7,20,62,193,608,1918,6061,19160,60582,191568,605782,1915640,

%T 6057776,19156359,60577716,191563545,605777108,1915635402

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

%C Asymptotically, the probability that a square begins with 1 is (sqrt(2)-1)/(sqrt(10)-1).

%C A generalization to arbitrary powers is found in Hürlimann, 2004. As the power increases, the probability distribution approaches Benford's law.

%H Robert Israel, <a href="/A083379/b083379.txt">Table of n, a(n) for n = 1..1999</a>

%H W. Hürlimann, <a href="http://www.ijpam.eu/contents/2004-11-1/4/4.pdf">Integer powers and Benford's law</a>, International Journal of Pure and Applied Mathematics, vol. 11, no. 1, pp. 39-46, 2004.

%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>

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

%Y Cf. A083377, A083378, A083380.

%K base,easy,nonn

%O 1,2

%A Werner S. Hürlimann (whurlimann(AT)bluewin.ch), Jun 05 2003

%E Edited by _Don Reble_, Nov 05 2005

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)