A111895 Number of numbers m <= n such that 5 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset

1,32

Comments

For n > 1: if A111862(n)=5 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) = 79, a(10000) = 934.

Crossrefs

Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111896, A111897, A111898, A111899, A111855.

Sequence in context: A064458 A125891 A153675 * A103379 A032550 A339172

Adjacent sequences: A111892 A111893 A111894 * A111896 A111897 A111898

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved