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A194464 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 A194464 #9 Feb 14 2021 21:40:26
%S A194464 5,10,13,14,15,18,19,20,26,31,34,35,36,39,40,41,47,52,68,73,89,94,99,
%T A194464 102,103,104,107,108,109,115,120,123,124,125,128,129,130,136,141,157,
%U A194464 162,178,183,188,191,192,193,196,197,198,204,209,212,213,214,217
%N A194464 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 A194464 See A194368.
%t A194464 r = GoldenRatio; c = FractionalPart[r/2];
%t A194464 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194464 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194464 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194464 Flatten[Position[t1, 1]]    (* A184463 *)
%t A194464 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194464 Flatten[Position[t3, 1]]    (* A184464 *)
%Y A194464 Cf. A194368.
%K A194464 nonn
%O A194464 1,1
%A A194464 _Clark Kimberling_, Aug 24 2011