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A279934 Positive integers k such that {(k-1)*r} > 1/2, where r = golden ratio = (1 + sqrt(5))/2 and { } = fractional part.

%I A279934 #9 Sep 15 2019 20:06:32
%S A279934 2,4,7,9,10,12,15,17,18,20,22,23,25,28,30,31,33,36,38,41,43,44,46,49,
%T A279934 51,52,54,56,57,59,62,64,65,67,70,72,75,77,78,80,83,85,86,88,91,93,96,
%U A279934 98,99,101,104,106,107,109,111,112,114,117,119,120
%N A279934 Positive integers k such that {(k-1)*r} > 1/2, where r = golden ratio = (1 + sqrt(5))/2 and { } = fractional part.
%H A279934 Clark Kimberling, <a href="/A279934/b279934.txt">Table of n, a(n) for n = 1..5000</a>
%F A279934 a(n) = 1 + A005652(n).
%t A279934 r = GoldenRatio;
%t A279934 t = Table[If[FractionalPart[n r - r] < 1/2, 0, 1 ], {n, 1, 120}] (* {A078588(n-1)} *)
%t A279934 Flatten[Position[t, 0]]  (* A279933 *)
%t A279934 Flatten[Position[t, 1]]  (* A279934 *)
%Y A279934 Cf. A005652, A279933 (complement).
%K A279934 nonn,easy
%O A279934 1,1
%A A279934 _Clark Kimberling_, Dec 23 2016
%E A279934 New name from _Jianing Song_, Sep 12 2019