%I #10 Feb 15 2021 02:20:29

%S 31,33,45,47,79,81,93,95,127,129,141,143,175,177,189,191,223,225,237,

%T 239,525,527,539,541,573,575,587,589,621,623,635,637,669,671,683,685,

%U 717,719,731,733

%N Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(7) and < > denotes fractional part.

%C See A194368.

%t r = Sqrt[7]; c = 1/2;

%t x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

%t y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

%t t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];

%t Flatten[Position[t1, 1]] (* A194378 *)

%t t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];

%t Flatten[Position[t2, 1]] (* A194379 *)

%t t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];

%t Flatten[Position[t3, 1]] (* A194380 *)

%Y Cf. A194368, A194378, A194379.

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 23 2011