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

1,4

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.

References

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

Links

Table of n, a(n) for n=1..86.

Example

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

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 *)

Crossrefs

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

Sequence in context: A178786 A350174 A000196 * A343265 A059396 A108602

Adjacent sequences: A111847 A111848 A111849 * A111851 A111852 A111853

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved