A111853 - OEIS

%I #11 Dec 24 2019 21:41:44

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

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

%U 6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9

%N Number of numbers m <= n such that 3 equals the first digit after decimal point of square root of n in decimal representation.

%C For n > 1: if A023961(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) = 0, a(100) = 9, a(1000) = 99, a(10000) = 990.

%t fddpQ[n_]:=Module[{a,b},{a,b}=RealDigits[Surd[n,2],10,10];a[[b+1]] == 3]; Accumulate[Table[If[fddpQ[n],1,0],{n,110}]] (* _Harvey P. Dale_, Feb 06 2019 *)

%Y Cf. A111850, A111851, A111852, A111854, A111855, A111856, A111857, A111858, A111859, A111893.

%K nonn,base

%O 1,19

%A _Reinhard Zumkeller_, Aug 20 2005