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A194206 a(n) = [Sum_{k=1..n} (k*Pi)], where [ ]=floor, ( )=fractional part. 3

%I

%S 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 15,16,16,17,18,19,19,19,19,20,21,21,22,22,23,23,24,24,25,26,26,26,27,

%U 27,28,29,29,30,30,30,31,31,32,33,33,33,34,34,35,35,36,36,37,37

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

%H G. C. Greubel, <a href="/A194206/b194206.txt">Table of n, a(n) for n = 1..5000</a>

%t r = Pi;

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

%t Table[a[n], {n, 1, 90}] (* A194206 *)

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

%t Table[s[n], {n, 1, 100}] (* A194207 *)

%o (PARI) a(n) = floor(sum(k=1, n, frac(Pi*k))); \\ _Michel Marcus_, Nov 12 2017

%Y Cf. A194207.

%K nonn

%O 1,5

%A _Clark Kimberling_, Aug 19 2011

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Last modified August 15 15:57 EDT 2020. Contains 336504 sequences. (Running on oeis4.)