A089809 Complement of A078588.

0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1

Offset: 1

Author

Gary W. Adamson, Nov 11 2003

Keywords

• nonn

Comments

a(n) = 1 if (fractional part of n*r) < 1/2, else a(n) = 0, where r = golden ratio = (1 + sqrt(5))/2. - Clark Kimberling, Dec 27 2016

Examples

			1. a(7) = 1 since A078588(7) = 0
2. a(7) = 1 since A024569 is not 1 (A024569(7) = 3).
3. a(7) = 1 since A089808(7) = 1.
		

Links

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

Crossrefs

Cf. A078588, A024569, A089808.

Programs

Mathematica

r = GoldenRatio; z = 500;
Table[If[FractionalPart[n r] < 1/2, 1, 0 ], {n, 1, z}]  (* A089809 *)
Table[If[FractionalPart[n r] > 1/2, 1, 0 ], {n, 1, z}]  (* A078588 *)
1 - % (* A089809,  Clark Kimberling, Dec 27 2016 *)

Python

from math import isqrt
def A089809(n): return ((n+isqrt(5*n**2))&1)^1 # Chai Wah Wu, Aug 17 2022

Formula

a(n) = 1 if A078588 = 0; otherwise, not.

a(n) = 1 iff A024569 is not 1.

a(n) = 1 iff A089808 is 1.

a(n) = 1 if (fractional part of n*r) < 1/2, else a(n) = 0. - Clark Kimberling, Dec 27 2016