This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A111853 #16 Aug 04 2025 13:24:15
%S A111853 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,
%T A111853 3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
%U A111853 6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
%N A111853 Number of numbers m <= n such that 3 equals the first digit after decimal point of square root of n in decimal representation.
%C A111853 For n > 1: if A023961(n)=3 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%C A111853 Lim_{n->infinity} a(n)/n = 1/10.
%D A111853 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H A111853 Harvey P. Dale, <a href="/A111853/b111853.txt">Table of n, a(n) for n = 1..1000</a>
%e A111853 a(10) = 0, a(100) = 9, a(1000) = 99, a(10000) = 990.
%t A111853 fddpQ[n_]:=Module[{a,b},{a,b}=RealDigits[Surd[n,2],10,10];a[[b+1]] == 3]; Accumulate[Table[If[fddpQ[n],1,0],{n,110}]] (* _Harvey P. Dale_, Feb 06 2019 *)
%t A111853 Accumulate[Table[If[NumberDigit[Sqrt[n],-1]==3,1,0],{n,110}]] (* _Harvey P. Dale_, Aug 04 2025 *)
%Y A111853 Cf. A111850, A111851, A111852, A111854, A111855, A111856, A111857, A111858, A111859, A111893.
%K A111853 nonn,base
%O A111853 1,19
%A A111853 _Reinhard Zumkeller_, Aug 20 2005