Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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