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A194399 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(15) and < > denotes fractional part.

%I A194399 #10 Feb 15 2021 02:19:05
%S A194399 6,8,14,16,22,24,30,32,38,40,46,48,54,56,62,70,78,86,94,102,110,118,
%T A194399 314,322,330,338,346,354,362,370,376,378,384,386,392,394,400,402,408,
%U A194399 410,416,418,424,426,432,434,438,442,446,450,454,458,462,466,470
%N A194399 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(15) and < > denotes fractional part.
%C A194399 Every term is even; see A194368.
%t A194399 r = Sqrt[15]; c = 1/2;
%t A194399 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194399 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194399 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194399 Flatten[Position[t1, 1]]       (* A194398 *)
%t A194399 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
%t A194399 Flatten[Position[t2, 1]]       (* A194399 *)
%t A194399 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
%t A194399 Flatten[Position[t3, 1]]       (* A194400 *)
%Y A194399 Cf. A010472, A194368, A194398, A194400.
%K A194399 nonn
%O A194399 1,1
%A A194399 _Clark Kimberling_, Aug 24 2011