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

Author

Reinhard Zumkeller, Aug 20 2005

Keywords

• nonn
• base

Examples

			a(10) = 1, a(100) = 11, a(1000) = 99, a(10000) = 1010.
		

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

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023961, A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111859, A111898.

Programs

Mathematica

Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 8] &, 100]] (* Paolo Xausa, May 17 2024 *)

Formula

For n > 1: if A023961(n) = 8 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

Limit_{n->oo} a(n)/n = 1/10.