A214988 Beatty sequence for sqrt(r), where r = (1+sqrt(5))/2 = golden ratio; complement of A214989.

1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 83, 85, 86

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Formula

a(n) = floor(t*n), where t=sqrt((1+sqrt(5))/2).

Example

a(1) = floor(t) = 1, a(2) = floor(2*t) = 2, where t=sqrt((1+sqrt(5))/2).

Mathematica

r = Sqrt[GoldenRatio]; s = r/(r - 1);
Table[Floor[r*n], {n, 1, 120}] (* A214988 *)
Table[Floor[s*n], {n, 1, 120}] (* A214989 *)

Crossrefs

Cf. A214989.

Sequence in context: A037459 A020654 A182777 * A028804 A345475 A191894

Adjacent sequences: A214985 A214986 A214987 * A214989 A214990 A214991

Keyword

nonn

Author

Clark Kimberling, Oct 28 2012

Status

approved