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A111852 Number of numbers m <= n such that 2 equals the first digit after decimal point of square root of n in decimal representation.

%I A111852 #11 May 17 2024 05:17:29
%S A111852 0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,
%T A111852 3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,
%U A111852 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10
%N A111852 Number of numbers m <= n such that 2 equals the first digit after decimal point of square root of n in decimal representation.
%C A111852 For n > 1: if A023961(n)=2 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%C A111852 Lim_{n->infinity} a(n)/n = 1/10.
%D A111852 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H A111852 Paolo Xausa, <a href="/A111852/b111852.txt">Table of n, a(n) for n = 1..10000</a>
%e A111852 a(10) = 1, a(100) = 9, a(1000) = 99, a(10000) = 990.
%t A111852 Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 2] &, 100]] (* _Paolo Xausa_, May 17 2024 *)
%Y A111852 Cf. A111850, A111851, A111853, A111854, A111855, A111856, A111857, A111858, A111859, A111892.
%K A111852 nonn,base
%O A111852 1,18
%A A111852 _Reinhard Zumkeller_, Aug 20 2005