A111892 - OEIS

%I #13 Nov 22 2021 15:28:58

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

%T 2,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,

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

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

%C For n > 1: if A111862(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 Harvey P. Dale, <a href="/A111892/b111892.txt">Table of n, a(n) for n = 1..1000</a>

%e a(10) = 1, a(100) = 7, a(1000) = 95, a(10000) = 1000.

%t Accumulate[Table[If[NumberDigit[Sqrt[n],-2]==2,1,0],{n,110}]] (* _Harvey P. Dale_, Nov 22 2021 *)

%Y Cf. A111862, A111890, A111891, A111893, A111894, A111895, A111896, A111897, A111898, A111899, A111852.

%K nonn,base

%O 1,17

%A _Reinhard Zumkeller_, Aug 20 2005