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A111855 Number of numbers m <= n such that 5 equals the first digit after decimal point of square root of n in decimal representation.

%I A111855 #14 May 17 2024 15:29:58
%S A111855 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,2,2,
%T A111855 2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,
%U A111855 4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7
%N A111855 Number of numbers m <= n such that 5 equals the first digit after decimal point of square root of n in decimal representation.
%D A111855 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H A111855 Paolo Xausa, <a href="/A111855/b111855.txt">Table of n, a(n) for n = 1..10000</a>
%F A111855 For n > 1: if A023961(n)=5 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%F A111855 Limit_{n->oo} a(n)/n = 1/10.
%e A111855 a(10) = 0, a(100) = 7, a(1000) = 93, a(10000) = 970.
%t A111855 Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 5] &, 100]] (* _Paolo Xausa_, May 17 2024 *)
%Y A111855 Cf. A111850, A111851, A111852, A111853, A111854, A111856, A111857, A111858, A111859, A111895.
%K A111855 nonn,base
%O A111855 1,31
%A A111855 _Reinhard Zumkeller_, Aug 20 2005