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A194372 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=sqrt(3) and < > denotes fractional part.

%I A194372 #13 Feb 15 2021 21:23:57
%S A194372 2,4,6,8,10,12,14,18,22,26,28,30,32,34,36,38,40,42,46,50,54,56,58,60,
%T A194372 62,64,66,68,70,74,78,82,84,86,88,90,92,94,96,98,102,106,110,112,114,
%U A194372 116,118,120,122,124,126,130,134,138,140,142,144,146,148,150,152
%N A194372 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(3) and < > denotes fractional part.
%C A194372 See A194368.
%H A194372 G. C. Greubel, <a href="/A194372/b194372.txt">Table of n, a(n) for n = 1..1000</a>
%t A194372 r = Sqrt[3]; c = 1/2;
%t A194372 x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
%t A194372 y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
%t A194372 t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 100}];
%t A194372 Flatten[Position[t1, 1]]  (* A194371 *)
%t A194372 t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];
%t A194372 Flatten[Position[t2, 1]] (* A194372 *)
%t A194372 t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
%t A194372 Flatten[Position[t3, 1]] (* A194373 *)
%Y A194372 Cf. A194368, A194371.
%K A194372 nonn
%O A194372 1,1
%A A194372 _Clark Kimberling_, Aug 23 2011