A024540 a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(2)} ), where {x} := x - floor(x).

2, 3, 7, 8, 22, 24, 25, 28, 29, 36, 37, 38, 40, 41, 45, 46, 70, 72, 73, 76, 77, 85, 86, 87, 89, 90, 95, 96, 178, 180, 181, 184, 185, 197, 199, 200, 203, 204, 210, 211, 212, 214, 215, 219, 220, 238, 240, 241, 244, 245, 253, 254, 255, 257, 258, 263, 264, 305, 307, 308, 311, 312, 322

Offset

1,1

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Formula

Partial sums of A024539. - Sean A. Irvine, Jul 13 2019

Maple

ListTools:-PartialSums([seq(floor(1/frac(k*sqrt(2))), k=1..100)]); # Robert Israel, Jul 14 2019

Mathematica

Table[Sum[Floor[1/FractionalPart[k*Sqrt[2]]], {k, 1, n}], {n, 1, 100}] (* Clark Kimberling, Aug 17 2012 *)

Prog

(Magma) a:=Sqrt(2); [&+[Floor(1/(k*a-Floor(k*a))):k in [1..n]]:n in [1..60]]; // Vincenzo Librandi, Jul 17 2019

Crossrefs

Cf. A024539.

Sequence in context: A276032 A114281 A137823 * A029785 A045545 A029790

Adjacent sequences: A024537 A024538 A024539 * A024541 A024542 A024543

Keyword

nonn

Author

Clark Kimberling

Status

approved