A111854 Number of numbers m <= n such that 4 equals the first digit after decimal point of square root of n in decimal representation.

0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13

Offset

1,6

Comments

For n > 1: if A023961(n)=4 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

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

Example

a(10) = 2, a(100) = 13, a(1000) = 112, a(10000) = 1030.

Mathematica

Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 4] &, 100]] (* Paolo Xausa, May 17 2024 *)

Crossrefs

Cf. A111850, A111851, A111852, A111853, A111855, A111856, A111857, A111858, A111859, A111894.

Sequence in context: A111651 A151982 A259361 * A132085 A111654 A264749

Adjacent sequences: A111851 A111852 A111853 * A111855 A111856 A111857

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved