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 A111851 #13 May 17 2024 15:29:48
%S A111851 0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,
%T A111851 3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,
%U A111851 7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,11
%N A111851 Number of numbers m <= n such that 1 equals the first digit after decimal point of square root of n in decimal representation.
%D A111851 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H A111851 Paolo Xausa, <a href="/A111851/b111851.txt">Table of n, a(n) for n = 1..10000</a>
%F A111851 For n > 1: if A023961(n)=1 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%F A111851 Limit_{n->oo} a(n)/n = 1/10.
%e A111851 a(10) = 1, a(100) = 9, a(1000) = 99, a(10000) = 990.
%t A111851 Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 1] &, 100]] (* _Paolo Xausa_, May 17 2024 *)
%Y A111851 Cf. A111850, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111859, A111891.
%K A111851 nonn,base
%O A111851 1,17
%A A111851 _Reinhard Zumkeller_, Aug 20 2005