The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A194198 [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(10). 2

%I

%S 0,0,0,1,2,3,3,3,4,4,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,12,13,13,14,

%T 15,15,15,16,16,17,18,18,18,18,19,19,20,21,21,21,22,23,23,24,24,25,25,

%U 26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,33,34,34,35,36

%N [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(10).

%H Robert Israel, <a href="/A194198/b194198.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n/2 by Weyl's equidistribution theorem. - _Robert Israel_, Jul 17 2019

%p map(floor,ListTools:-PartialSums([seq(frac(k*sqrt(10)),k=1..100)])); # _Robert Israel_, Jul 17 2019

%t r = Sqrt[10];

%t a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]

%t Table[a[n], {n, 1, 90}] (* A194198 *)

%t s[n_] := Sum[a[k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}] (* A194199 *)

%Y Cf. A194199.

%K nonn

%O 1,5

%A _Clark Kimberling_, Aug 19 2011

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

Last modified December 4 15:14 EST 2021. Contains 349526 sequences. (Running on oeis4.)