A111858 Number of numbers m <= n such that 8 equals the first digit after decimal point of square root of n in decimal representation.

0, 0, 0, 0, 0, 0, 0, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 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

Offset

1,15

Comments

For n > 1: if A023961(n)=8 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) = 1, a(100) = 11, a(1000) = 99, a(10000) = 1010.

Crossrefs

Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111859, A111898.

Sequence in context: A245636 A171622 A351846 * A111856 A111857 A133879

Adjacent sequences: A111855 A111856 A111857 * A111859 A111860 A111861

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved