A194198 [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(10).

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, 15, 15, 15, 16, 16, 17, 18, 18, 18, 18, 19, 19, 20, 21, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 33, 34, 34, 35, 36

Offset

1,5

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ n/2 by Weyl's equidistribution theorem. - Robert Israel, Jul 17 2019

Maple

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

Mathematica

r = Sqrt[10];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]  (* A194198 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194199 *)

Crossrefs

Cf. A194199.

Sequence in context: A244989 A296021 A267097 * A189674 A156250 A029108

Adjacent sequences: A194195 A194196 A194197 * A194199 A194200 A194201

Keyword

nonn

Author

Clark Kimberling, Aug 19 2011

Status

approved