A111852 - OEIS

%I #11 May 17 2024 05:17:29

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

%T 3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,

%U 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10

%N Number of numbers m <= n such that 2 equals the first digit after decimal point of square root of n in decimal representation.

%C For n > 1: if A023961(n)=2 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.

%H Paolo Xausa, <a href="/A111852/b111852.txt">Table of n, a(n) for n = 1..10000</a>

%e a(10) = 1, a(100) = 9, a(1000) = 99, a(10000) = 990.

%t Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 2] &, 100]] (* _Paolo Xausa_, May 17 2024 *)

%Y Cf. A111850, A111851, A111853, A111854, A111855, A111856, A111857, A111858, A111859, A111892.

%K nonn,base

%O 1,18

%A _Reinhard Zumkeller_, Aug 20 2005