

A194206


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


3



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
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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



