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A194462 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 A194462 #9 Feb 14 2021 21:40:41
%S A194462 1,2,4,5,7,10,13,14,15,17,18,20,23,26,27,28,30,31,33,34,35,36,37,38,
%T A194462 39,40,41,43,44,46,47,48,49,50,51,52,53,54,56,57,59,60,62,65,68,69,70,
%U A194462 72,73,75,78,81,82,83,85,86,88,89,90,91,92,93,94,95,96,98,99,101
%N A194462 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 A194462 See A194368.
%t A194462 r = GoldenRatio; c = (1/2) FractionalPart[r];
%t A194462 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194462 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194462 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194462 Flatten[Position[t1, 1]]  (* A184461 *)
%t A194462 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194462 Flatten[Position[t3, 1]]  (* A184462 *)
%Y A194462 Cf. A194368.
%K A194462 nonn
%O A194462 1,2
%A A194462 _Clark Kimberling_, Aug 24 2011