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A194396 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(14) and < > denotes fractional part.

%I A194396 #10 Feb 15 2021 02:18:46
%S A194396 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,34,38,42,46,50,54,58,60,62,
%T A194396 64,66,68,70,72,74,76,78,80,82,84,86,88,90,94,98,102,106,110,114,118,
%U A194396 120,122,124,126,128,130,132,134,136,138,140,142,144,146,148,150
%N A194396 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(14) and < > denotes fractional part.
%C A194396 Every term is even; see A194368.
%t A194396 r = Sqrt[14]; c = 1/2;
%t A194396 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194396 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194396 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 200}];
%t A194396 Flatten[Position[t1, 1]]       (* A194395 *)
%t A194396 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
%t A194396 Flatten[Position[t2, 1]]       (* A194396 *)
%t A194396 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
%t A194396 Flatten[Position[t3, 1]]       (* A194397 *)
%Y A194396 Cf. A010471, A194368, A194395, A194397.
%K A194396 nonn
%O A194396 1,1
%A A194396 _Clark Kimberling_, Aug 23 2011