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%I #15 Aug 17 2022 22:20:39
%S 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,
%T 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
%N Complement of A078588.
%C 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
%H Clark Kimberling, <a href="/A089809/b089809.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 1 if A078588 = 0; otherwise, not.
%F a(n) = 1 iff A024569 is not 1.
%F a(n) = 1 iff A089808 is 1.
%F a(n) = 1 if (fractional part of n*r) < 1/2, else a(n) = 0. - _Clark Kimberling_, Dec 27 2016
%e 1. a(7) = 1 since A078588(7) = 0
%e 2. a(7) = 1 since A024569 is not 1 (A024569(7) = 3).
%e 3. a(7) = 1 since A089808(7) = 1.
%t r = GoldenRatio; z = 500;
%t Table[If[FractionalPart[n r] < 1/2, 1, 0 ], {n, 1, z}] (* A089809 *)
%t Table[If[FractionalPart[n r] > 1/2, 1, 0 ], {n, 1, z}] (* A078588 *)
%t 1 - % (* A089809, _Clark Kimberling_, Dec 27 2016 *)
%o (Python)
%o from math import isqrt
%o def A089809(n): return ((n+isqrt(5*n**2))&1)^1 # _Chai Wah Wu_, Aug 17 2022
%Y Cf. A078588, A024569, A089808.
%K nonn
%O 1,1
%A _Gary W. Adamson_, Nov 11 2003
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