A194206 a(n) = [Sum_{k=1..n} (k*Pi)], where [ ]=floor, ( )=fractional part.

0, 0, 0, 1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 15, 16, 16, 17, 18, 19, 19, 19, 19, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 26, 26, 26, 27, 27, 28, 29, 29, 30, 30, 30, 31, 31, 32, 33, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Mathematica

r = Pi;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]  (* A194206 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A194207 *)

Prog

(PARI) a(n) = floor(sum(k=1, n, frac(Pi*k))); \\ Michel Marcus, Nov 12 2017

Crossrefs

Cf. A194207.

Sequence in context: A269990 A324473 A159481 * A307482 A046699 A239105

Adjacent sequences: A194203 A194204 A194205 * A194207 A194208 A194209

Keyword

nonn

Author

Clark Kimberling, Aug 19 2011

Status

approved