cp's OEIS Frontend

A111899 Number of numbers m <= n such that 9 equals the second digit after decimal point of square root of n in decimal representation.

%I A111899 #17 May 18 2024 01:54:24
%S A111899 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,3,4,5,6,6,6,6,6,6,6,
%T A111899 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U A111899 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,8,8,9,9,10,10,10,10,11
%N A111899 Number of numbers m <= n such that 9 equals the second digit after decimal point of square root of n in decimal representation.
%D A111899 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H A111899 Paolo Xausa, <a href="/A111899/b111899.txt">Table of n, a(n) for n = 1..10000</a>
%F A111899 For n > 1: if A111862(n) = 9 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%F A111899 Limit_{n->oo} a(n)/n = 1/10.
%e A111899 a(10) = 0, a(100) = 10, a(1000) = 106, a(10000) = 994.
%t A111899 Accumulate[Array[Boole[Mod[Floor[100*Sqrt[#]], 10] == 9] &, 100]] (* _Paolo Xausa_, May 17 2024 *)
%Y A111899 Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111859.
%K A111899 nonn,base
%O A111899 1,23
%A A111899 _Reinhard Zumkeller_, Aug 20 2005