A111892 Number of numbers m <= n such that 2 equals the second 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, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 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, 7, 7, 7

Offset

1,17

Comments

For n > 1: if A111862(n)=2 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) = 7, a(1000) = 95, a(10000) = 1000.

Mathematica

Accumulate[Table[If[NumberDigit[Sqrt[n], -2]==2, 1, 0], {n, 110}]] (* Harvey P. Dale, Nov 22 2021 *)

Crossrefs

Cf. A111862, A111890, A111891, A111893, A111894, A111895, A111896, A111897, A111898, A111899, A111852.

Sequence in context: A111891 A296076 A086858 * A108248 A087104 A343743

Adjacent sequences: A111889 A111890 A111891 * A111893 A111894 A111895

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved