%I #11 Mar 31 2022 12:13:36
%S 0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,7,7,7,7,7,
%U 7,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10
%N Number of numbers m <= n such that 1 equals the second digit after decimal point of square root of n in decimal representation.
%C For n > 1: if A111862(n)=1 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) = 1, a(100) = 10, a(1000) = 100, a(10000) = 998.
%t Accumulate[Table[If[NumberDigit[Sqrt[n],-2]==1,1,0],{n,100}]] (* _Harvey P. Dale_, Mar 31 2022 *)
%Y Cf. A111862, A111890, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111899, A111851.
%K nonn,base
%O 1,11
%A _Reinhard Zumkeller_, Aug 20 2005
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