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%I #17 May 17 2024 19:48:55
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,
%U 3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5
%N Number of numbers m <= n such that 9 equals the first digit after decimal point of square root of n in decimal representation.
%D G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H Paolo Xausa, <a href="/A111859/b111859.txt">Table of n, a(n) for n = 1..10000</a>
%F For n > 1: if A023961(n) = 9 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%F Limit_{n->oo} a(n)/n = 1/10.
%e a(10) = 0, a(100) = 5, a(1000) = 81, a(10000) = 950.
%t Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 9] &, 100]] (* _Paolo Xausa_, May 17 2024 *)
%Y Cf. A023961, A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111899.
%K nonn,base
%O 1,48
%A _Reinhard Zumkeller_, Aug 20 2005
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