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a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(5)} ), where {x} := x - floor(x).
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%I #19 Sep 08 2022 08:44:48

%S 4,6,7,8,13,15,16,17,25,27,28,29,43,46,47,48,124,128,130,131,132,137,

%T 139,140,141,148,150,151,152,164,167,168,169,207,210,212,213,214,218,

%U 220,221,222,228,230,231,232,242,245,246,247,272,275,276,277,278,282,284,285,286

%N a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(5)} ), where {x} := x - floor(x).

%H Clark Kimberling, <a href="/A024554/b024554.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[Sum[Floor[1/FractionalPart[k*Sqrt[5]]], {k, 1, n}], {n, 1, 100}]

%t (* _Clark Kimberling_, Aug 16 2012 *)

%o (Magma)a:=Sqrt(5);[&+[Floor(1/(k*a-Floor(k*a))):k in [1..n]]:n in [1..59]]; // _Marius A. Burtea_, Jul 16 2019

%Y Cf. A024555. Partial sums of A024553.

%K nonn

%O 1,1

%A _Clark Kimberling_