login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111850 Number of numbers m <= n such that 0 equals the first digit after decimal point of square root of n in decimal representation. 11
1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 14, 14, 14, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For n > 1: if A023961(n)=0 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..86.

EXAMPLE

a(10) = 3, a(100) = 15, a(1000) = 118, a(10000) = 1050.

MATHEMATICA

zd[n_]:=Module[{c=RealDigits[Sqrt[n], 10, 10], f}, f=Last[c]+1; If[First[c][[f]]==0, 1, 0]]; Accumulate[Array[zd, 90]] (* Harvey P. Dale, Feb 01 2012 *)

CROSSREFS

Cf. A111851, A111852, A111853, A111854, A111855, A111856, A111857, A111858, A111859, A111890.

Sequence in context: A178786 A350174 A000196 * A343265 A059396 A108602

Adjacent sequences: A111847 A111848 A111849 * A111851 A111852 A111853

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Aug 20 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)