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A194404 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) > 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.

%I A194404 #11 Feb 15 2021 02:19:21
%S A194404 5,7,13,15,39,41,47,49,73,75,81,83,89,91,93,94,95,96,97,99,101,102,
%T A194404 103,104,105,107,109,115,117,123,125,127,128,129,130,131,133,135,136,
%U A194404 137,138,139,141,143,149,151,157,159,183,185,191,193,217,219,225
%N A194404 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.
%C A194404 See A194368.
%t A194404 r = GoldenRatio; c = 1/2;
%t A194404 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194404 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194404 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194404 Flatten[Position[t1, 1]]       (* A194401 *)
%t A194404 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194404 Flatten[Position[t2, 1]]       (* A194402 *)
%t A194404 %/2       (* A194403 *)
%t A194404 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
%t A194404 Flatten[Position[t3, 1]]       (* A194404 *)
%Y A194404 Cf. A001622, A194368, A194401, A194402, A194403.
%K A194404 nonn
%O A194404 1,1
%A A194404 _Clark Kimberling_, Aug 24 2011