A111859 Number of numbers m <= n such that 9 equals the first digit after decimal point of square root of n in decimal representation.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5

Offset

1,48

Comments

For n > 1: if A023961(n)=9 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..105.

Example

a(10) = 0, a(100) = 5, a(1000) = 81, a(10000) = 950.

Crossrefs

Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111899.

Sequence in context: A355478 A097876 A177830 * A156822 A130635 A107609

Adjacent sequences: A111856 A111857 A111858 * A111860 A111861 A111862

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved