A111899 Number of numbers m <= n such that 9 equals the second 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, 1, 2, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 10, 11

Offset

1,23

Comments

For n > 1: if A111862(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..102.

Example

a(10) = 0, a(100) = 10, a(1000) = 106, a(10000) = 994.

Crossrefs

Cf. A111890, A111891, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111859.

Sequence in context: A333527 A064047 A335152 * A074753 A013928 A172104

Adjacent sequences: A111896 A111897 A111898 * A111900 A111901 A111902

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved