A111897 - OEIS

%I #11 Dec 25 2019 08:33:54

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,

%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,

%U 5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7

%N Number of numbers m <= n such that 7 equals the second digit after decimal point of square root of n in decimal representation.

%C For n > 1: if A111862(n)=7 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) = 0, a(100) = 7, a(1000) = 100, a(10000) = 1000.

%t Accumulate[Table[If[Mod[IntegerPart[100*Sqrt[n]],10]==7,1,0],{n,110}]] (* _Harvey P. Dale_, Oct 16 2014 *)

%Y Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111895, A111896, A111898, A111899, A111857.

%K nonn,base

%O 1,20

%A _Reinhard Zumkeller_, Aug 20 2005