cp's OEIS Frontend

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

%I A194206 #12 Nov 12 2017 03:03:19
%S A194206 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,
%T A194206 15,16,16,17,18,19,19,19,19,20,21,21,22,22,23,23,24,24,25,26,26,26,27,
%U A194206 27,28,29,29,30,30,30,31,31,32,33,33,33,34,34,35,35,36,36,37,37
%N A194206 a(n) = [Sum_{k=1..n} (k*Pi)], where [ ]=floor, ( )=fractional part.
%H A194206 G. C. Greubel, <a href="/A194206/b194206.txt">Table of n, a(n) for n = 1..5000</a>
%t A194206 r = Pi;
%t A194206 a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
%t A194206 Table[a[n], {n, 1, 90}]  (* A194206 *)
%t A194206 s[n_] := Sum[a[k], {k, 1, n}]
%t A194206 Table[s[n], {n, 1, 100}] (* A194207 *)
%o A194206 (PARI) a(n) = floor(sum(k=1, n, frac(Pi*k))); \\ _Michel Marcus_, Nov 12 2017
%Y A194206 Cf. A194207.
%K A194206 nonn
%O A194206 1,5
%A A194206 _Clark Kimberling_, Aug 19 2011