A111891 Number of numbers m <= n such that 1 equals the second digit after decimal point of square root of n in decimal representation.

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, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

1,11

Comments

For n > 1: if A111862(n)=1 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

Table of n, a(n) for n=1..98.

Example

a(10) = 1, a(100) = 10, a(1000) = 100, a(10000) = 998.

Mathematica

Accumulate[Table[If[NumberDigit[Sqrt[n], -2]==1, 1, 0], {n, 100}]] (* Harvey P. Dale, Mar 31 2022 *)

Crossrefs

Cf. A111862, A111890, A111892, A111893, A111894, A111895, A111896, A111897, A111898, A111899, A111851.

Sequence in context: A073458 A194698 A105519 * A296076 A086858 A111892

Adjacent sequences: A111888 A111889 A111890 * A111892 A111893 A111894

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved