A111893 Number of numbers m <= n such that 3 equals the second digit after decimal point of square root of n in decimal representation.

0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 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, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset

1,5

Comments

For n > 1: if A111862(n)=3 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) = 2, a(100) = 8, a(1000) = 103, a(10000) = 1000.

Mathematica

Accumulate[Table[If[Mod[Floor[100N[Sqrt[n], 10]], 10]==3, 1, 0], {n, 120}]] (* Harvey P. Dale, Mar 04 2015 *)

Crossrefs

Cf. A111862, A111890, A111891, A111892, A111894, A111895, A111896, A111897, A111898, A111899, A111853.

Sequence in context: A235044 A163857 A185715 * A121902 A087103 A287091

Adjacent sequences: A111890 A111891 A111892 * A111894 A111895 A111896

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved