cp's OEIS Frontend

A111857 Number of numbers m <= n such that 7 equals the first digit after decimal point of square root of n in decimal representation.

%I A111857 #11 Apr 20 2022 12:42:07
%S A111857 0,0,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,
%T A111857 4,4,4,4,4,4,4,4,4,4,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,
%U A111857 7,7,7,7,7,7,7,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,11,11,11,11,11,11
%N A111857 Number of numbers m <= n such that 7 equals the first digit after decimal point of square root of n in decimal representation.
%C A111857 For n > 1: if A023961(n)=7 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).
%C A111857 Lim_{n->infinity} a(n)/n = 1/10.
%D A111857 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.
%H A111857 Harvey P. Dale, <a href="/A111857/b111857.txt">Table of n, a(n) for n = 1..1000</a>
%e A111857 a(10) = 1, a(100) = 11, a(1000) = 99, a(10000) = 1010.
%t A111857 Accumulate[Table[If[NumberDigit[Sqrt[n],-1]==7,1,0],{n,120}]] (* _Harvey P. Dale_, Apr 20 2022 *)
%Y A111857 Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111858, A111859, A111897.
%K A111857 nonn,base
%O A111857 1,14
%A A111857 _Reinhard Zumkeller_, Aug 20 2005