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A089809
Complement of A078588.
4
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
1,1
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
LINKS
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
EXAMPLE
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.
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 *)
PROG
(Python)
from math import isqrt
def A089809(n): return ((n+isqrt(5*n**2))&1)^1 # Chai Wah Wu, Aug 17 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Nov 11 2003
STATUS
approved