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%I #11 Dec 25 2019 08:33:17
%S 0,0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,
%T 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,
%U 5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8
%N Number of numbers m <= n such that 3 equals the second digit after decimal point of square root of n in decimal representation.
%C For n > 1: if A111862(n)=3 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%C Lim_{n->infinity} a(n)/n = 1/10.
%D G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%e a(10) = 2, a(100) = 8, a(1000) = 103, a(10000) = 1000.
%t Accumulate[Table[If[Mod[Floor[100N[Sqrt[n],10]],10]==3,1,0],{n,120}]] (* _Harvey P. Dale_, Mar 04 2015 *)
%Y Cf. A111862, A111890, A111891, A111892, A111894, A111895, A111896, A111897, A111898, A111899, A111853.
%K nonn,base
%O 1,5
%A _Reinhard Zumkeller_, Aug 20 2005
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