A194212 - OEIS

A194212

a(n) = floor(Sum_{k=1..n} <2*k*Pi>), where < > = fractional part.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..73.

MATHEMATICA

r = 2Pi;

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

Table[a[n], {n, 1, 90}] (* A194212 *)

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

Table[s[n], {n, 1, 100}] (* A194213 *)

CROSSREFS