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 A111896 Number of numbers m <= n such that 6 equals the second digit after decimal point of square root of n in decimal representation. 11

%I

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

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

%U 5,6,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N Number of numbers m <= n such that 6 equals the second digit after decimal point of square root of n in decimal representation.

%C For n > 1: if A111862(n)=6 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) = 1, a(100) = 8, a(1000) = 98, a(10000) = 1000.

%t sd6Q[n_]:=Module[{c=RealDigits[Sqrt[n],10,10]},If[Drop[c[[1]],c[[2]]][[2]]==6,1,0]]; Accumulate[Array[sd6Q,110]] (* _Harvey P. Dale_, Aug 17 2012 *)

%Y Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111895, A111897, A111898, A111899, A111856.

%K nonn,base

%O 1,12

%A _Reinhard Zumkeller_, Aug 20 2005

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Last modified May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)