A279934 Positive integers k such that {(k-1)*r} > 1/2, where r = golden ratio = (1 + sqrt(5))/2 and { } = fractional part.

2, 4, 7, 9, 10, 12, 15, 17, 18, 20, 22, 23, 25, 28, 30, 31, 33, 36, 38, 41, 43, 44, 46, 49, 51, 52, 54, 56, 57, 59, 62, 64, 65, 67, 70, 72, 75, 77, 78, 80, 83, 85, 86, 88, 91, 93, 96, 98, 99, 101, 104, 106, 107, 109, 111, 112, 114, 117, 119, 120

Offset

1,1

Links

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

Formula

a(n) = 1 + A005652(n).

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 *)

Crossrefs

Cf. A005652, A279933 (complement).

Sequence in context: A081249 A327217 A327207 * A047541 A308496 A226812

Adjacent sequences: A279931 A279932 A279933 * A279935 A279936 A279937

Keyword

nonn,easy

Author

Clark Kimberling, Dec 23 2016

Extensions

New name from Jianing Song, Sep 12 2019

Status

approved