A111855 Number of numbers m <= n such that 5 equals the first 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, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 4, 4, 4, 4, 5, 5, 5, 5, 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

Offset

1,31

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

Formula

For n > 1: if A023961(n)=5 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

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

Example

a(10) = 0, a(100) = 7, a(1000) = 93, a(10000) = 970.

Mathematica

Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 5] &, 100]] (* Paolo Xausa, May 17 2024 *)

Crossrefs

Cf. A111850, A111851, A111852, A111853, A111854, A111856, A111857, A111858, A111859, A111895.

Sequence in context: A105209 A179076 A095861 * A071701 A342696 A064459

Adjacent sequences: A111852 A111853 A111854 * A111856 A111857 A111858

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved