A111856 Number of numbers m <= n such that 6 equals the first digit after decimal point of square root of n in decimal representation.

0, 0, 0, 0, 0, 0, 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, 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, 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, 11, 11, 11

Offset

1,13

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)=6 then a(n) = a(n-1) + 1, otherwise a(n) = a(n-1).

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

Example

a(10) = 1, a(100) = 11, a(1000) = 101, a(10000) = 1010.

Mathematica

Accumulate[Array[Boole[Mod[Floor[10*Sqrt[#]], 10] == 6] &, 100]] (* Paolo Xausa, May 17 2024 *)

Crossrefs

Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111857, A111858, A111859, A111896.

Sequence in context: A171622 A351846 A111858 * A111857 A133879 A343609

Adjacent sequences: A111853 A111854 A111855 * A111857 A111858 A111859

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved