A120753 Numbers k such that {rk} > c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.

1, 4, 5, 7, 8, 11, 14, 15, 18, 21, 22, 24, 25, 28, 29, 31, 32, 35, 38, 39, 41, 42, 45, 46, 48, 49, 52, 55, 56, 59, 62, 63, 65, 66, 69, 72, 73, 76, 79, 80, 82, 83, 86, 87, 89, 90, 93, 96, 97, 100, 103, 104, 106, 107, 110, 113, 114, 117, 120, 121, 123, 124, 127, 128, 130, 131

Offset

1,2

Comments

Positions of 1 in A083035.

Links

Table of n, a(n) for n=1..66.

Example

(See A120243.)

Mathematica

r = Sqrt[1/2]; b = 2; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A083035 *)
Flatten[Position[t, 0]]      (* A120752 *)
Flatten[Position[t, 1]]      (* A120753 *)
With[{c=Sqrt[1/2]}, Select[Range[150], FractionalPart[c #]>1/2&]] (* Harvey P. Dale, Dec 21 2025 *)

Crossrefs

Cf. A083035, A120752, A190762.

Sequence in context: A032702 A359380 A356160 * A188322 A139201 A049649

Adjacent sequences: A120750 A120751 A120752 * A120754 A120755 A120756

Keyword

nonn

Author

Clark Kimberling, Jul 01 2006

Status

approved