A279933 Positive integers k such that {(k-1)*r} < 1/2, where r = golden ratio = (1 + sqrt(5))/2 and { } = fractional part.

1, 3, 5, 6, 8, 11, 13, 14, 16, 19, 21, 24, 26, 27, 29, 32, 34, 35, 37, 39, 40, 42, 45, 47, 48, 50, 53, 55, 58, 60, 61, 63, 66, 68, 69, 71, 73, 74, 76, 79, 81, 82, 84, 87, 89, 90, 92, 94, 95, 97, 100, 102, 103, 105, 108, 110, 113, 115, 116, 118

Offset: 1

Author

Clark Kimberling, Dec 23 2016

Keywords

• nonn
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A005653, A279934 (complement).

Programs

Mathematica

r = GoldenRatio;
t = Table[If[FractionalPart[n r - r] < 1/2, 0, 1 ], {n, 1, 120}] (* {A078588(n-1)} *)
Flatten[Position[t, 0]]  (* A279933 *)
Flatten[Position[t, 1]]  (* A279934 *)

Formula

a(n) = 1 + A005653(n-1) for n > 1.

Extensions

New name from Jianing Song, Sep 12 2019