|
%I #23 Sep 08 2022 08:44:48
%S 2,3,7,8,22,24,25,28,29,36,37,38,40,41,45,46,70,72,73,76,77,85,86,87,
%T 89,90,95,96,178,180,181,184,185,197,199,200,203,204,210,211,212,214,
%U 215,219,220,238,240,241,244,245,253,254,255,257,258,263,264,305,307,308,311,312,322
%N a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(2)} ), where {x} := x - floor(x).
%H Clark Kimberling, <a href="/A024540/b024540.txt">Table of n, a(n) for n = 1..1000</a>
%F Partial sums of A024539. - _Sean A. Irvine_, Jul 13 2019
%p ListTools:-PartialSums([seq(floor(1/frac(k*sqrt(2))),k=1..100)]); # _Robert Israel_, Jul 14 2019
%t Table[Sum[Floor[1/FractionalPart[k*Sqrt[2]]], {k, 1, n}], {n, 1, 100}] (* _Clark Kimberling_, Aug 17 2012 *)
%o (Magma) a:=Sqrt(2); [&+[Floor(1/(k*a-Floor(k*a))):k in [1..n]]:n in [1..60]]; // _Vincenzo Librandi_, Jul 17 2019
%Y Cf. A024539.
%K nonn
%O 1,1
%A _Clark Kimberling_
|
