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

1,2

Links

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

Formula

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

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. A005653, A279934 (complement).

Sequence in context: A309544 A154111 A047444 * A327206 A212439 A160734

Adjacent sequences: A279930 A279931 A279932 * A279934 A279935 A279936

Keyword

nonn,easy

Author

Clark Kimberling, Dec 23 2016

Extensions

New name from Jianing Song, Sep 12 2019

Status

approved