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 A111856 #13 May 17 2024 15:27:39
%S A111856 0,0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,
%T A111856 4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,
%U A111856 7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,11,11,11,11,11,11,11,11
%N A111856 Number of numbers m <= n such that 6 equals the first digit after decimal point of square root of n in decimal representation.
%D A111856 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H A111856 Paolo Xausa, <a href="/A111856/b111856.txt">Table of n, a(n) for n = 1..10000</a>
%F A111856 For n > 1: if A023961(n)=6 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%F A111856 Limit_{n->oo} a(n)/n = 1/10.
%e A111856 a(10) = 1, a(100) = 11, a(1000) = 101, a(10000) = 1010.
%t A111856 Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 6] &, 100]] (* _Paolo Xausa_, May 17 2024 *)
%Y A111856 Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111857, A111858, A111859, A111896.
%K A111856 nonn,base
%O A111856 1,13
%A A111856 _Reinhard Zumkeller_, Aug 20 2005