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A194379 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(7) and < > denotes fractional part.

%I A194379 #9 Feb 16 2021 01:03:34
%S A194379 2,14,16,28,30,32,34,36,42,44,46,48,50,62,64,76,78,80,82,84,90,92,94,
%T A194379 96,98,110,112,124,126,128,130,132,138,140,142,144,146,158,160,172,
%U A194379 174,176,178,180,186,188,190,192,194,206,208,220,222,224,226,228
%N A194379 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(7) and < > denotes fractional part.
%C A194379 All the terms are even.  See A194368.
%e A194379 r = Sqrt[7]; c = 1/2;
%t A194379 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194379 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194379 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194379 Flatten[Position[t1, 1]]   (* A194378 *)
%t A194379 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
%t A194379 Flatten[Position[t2, 1]]  (* A194379 *)
%t A194379 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
%t A194379 Flatten[Position[t3, 1]]   (* A194380 *)
%Y A194379 Cf. A194368.
%K A194379 nonn
%O A194379 1,1
%A A194379 _Clark Kimberling_, Aug 23 2011