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A194463 Numbers m such that Sum_{k=1..m} ( - ) < 0, where r=(1+sqrt(5))/2 and c=(1+sqrt(5))/4, and < > denotes fractional part.

%I A194463 #9 Feb 14 2021 21:40:35
%S A194463 1,2,3,4,6,7,8,9,11,12,16,17,21,22,23,24,25,27,28,29,30,32,33,37,38,
%T A194463 42,43,44,45,46,48,49,50,51,53,54,55,56,57,58,59,60,61,62,63,64,65,66,
%U A194463 67,69,70,71,72,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,90
%N A194463 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) < 0, where r=(1+sqrt(5))/2 and c=(1+sqrt(5))/4, and < > denotes fractional part.
%C A194463 See A194368.
%t A194463 r = GoldenRatio; c = FractionalPart[r/2];
%t A194463 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194463 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194463 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194463 Flatten[Position[t1, 1]]    (* A184463 *)
%t A194463 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194463 Flatten[Position[t3, 1]]    (* A184464 *)
%Y A194463 Cf. A194368.
%K A194463 nonn
%O A194463 1,2
%A A194463 _Clark Kimberling_, Aug 24 2011