A111897 Number of numbers m <= n such that 7 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, 1, 1, 1, 1, 1, 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, 3, 3, 3, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset

1,20

Comments

For n > 1: if A111862(n)=7 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) = 7, a(1000) = 100, a(10000) = 1000.

Mathematica

Accumulate[Table[If[Mod[IntegerPart[100*Sqrt[n]], 10]==7, 1, 0], {n, 110}]] (* Harvey P. Dale, Oct 16 2014 *)

Crossrefs

Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111895, A111896, A111898, A111899, A111857.

Sequence in context: A064601 A262303 A127321 * A185711 A185712 A328499

Adjacent sequences: A111894 A111895 A111896 * A111898 A111899 A111900

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved