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%I #10 Dec 24 2019 21:41:25
%S 1,1,1,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,6,6,6,6,6,6,6,6,6,
%T 6,7,8,8,8,8,8,8,8,8,8,8,8,8,9,10,10,10,10,10,10,10,10,10,10,10,10,10,
%U 10,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,14,14,14,14,14
%N Number of numbers m <= n such that 0 equals the first digit after decimal point of square root of n in decimal representation.
%C For n > 1: if A023961(n)=0 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%C Lim_{n->infinity} a(n)/n = 1/10.
%D G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%e a(10) = 3, a(100) = 15, a(1000) = 118, a(10000) = 1050.
%t zd[n_]:=Module[{c=RealDigits[Sqrt[n],10,10],f},f=Last[c]+1;If[First[c][[f]]==0,1,0]]; Accumulate[Array[zd,90]] (* _Harvey P. Dale_, Feb 01 2012 *)
%Y Cf. A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111859, A111890.
%K nonn,base
%O 1,4
%A _Reinhard Zumkeller_, Aug 20 2005
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