A111893 - 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