A111857 Number of numbers m <= n such that 7 equals the first digit after decimal point of square root of n in decimal representation.

0, 0, 1, 1, 1, 1, 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, 5, 6, 6, 6, 6, 6, 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, 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

Offset

1,14

Comments

For n > 1: if A023961(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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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

Mathematica

Accumulate[Table[If[NumberDigit[Sqrt[n], -1]==7, 1, 0], {n, 120}]] (* Harvey P. Dale, Apr 20 2022 *)

Crossrefs

Cf. A111850, A111851, A111852, A111853, A111854, A111855, A111856, A111858, A111859, A111897.

Sequence in context: A351846 A111858 A111856 * A133879 A343609 A054898

Adjacent sequences: A111854 A111855 A111856 * A111858 A111859 A111860

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved