A111896 Number of numbers m <= n such that 6 equals the second digit after decimal point of square root of n in decimal representation.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset

1,12

Comments

For n > 1: if A111862(n)=6 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..105.

Example

a(10) = 1, a(100) = 8, a(1000) = 98, a(10000) = 1000.

Mathematica

sd6Q[n_]:=Module[{c=RealDigits[Sqrt[n], 10, 10]}, If[Drop[c[[1]], c[[2]]][[2]]==6, 1, 0]]; Accumulate[Array[sd6Q, 110]] (* Harvey P. Dale, Aug 17 2012 *)

Crossrefs

Cf. A111862, A111890, A111891, A111892, A111893, A111894, A111895, A111897, A111898, A111899, A111856.

Sequence in context: A048766 A105516 A105518 * A105515 A105514 A214081

Adjacent sequences: A111893 A111894 A111895 * A111897 A111898 A111899

Keyword

nonn,base

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved