A111850 Number of numbers m <= n such that 0 equals the first digit after decimal point of square root of n in decimal representation.

1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14

Offset: 1

Author

Reinhard Zumkeller, Aug 20 2005

Keywords

• nonn
• base

Comments

For n > 1: if A023961(n)=0 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Lim_{n->infinity} a(n)/n = 1/10.

Examples

			a(10) = 3, a(100) = 15, a(1000) = 118, a(10000) = 1050.
		

References

• G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Two, Chap. 4, Sect. 4, Problem 178.

Crossrefs

Cf. A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111859, A111890.

Programs

Mathematica

zd[n_]:=Module[{c=RealDigits[Sqrt[n],10,10],f},f=Last[c]+1;If[First[c][[f]]==0,1,0]]; Accumulate[Array[zd,90]] (* Harvey P. Dale, Feb 01 2012 *)