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A194376
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Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(6) and < > denotes fractional part.
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3
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2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 198, 200, 202, 204, 206, 218, 220, 222, 224, 226, 238, 240, 242, 244, 246, 258, 260, 262, 264, 266, 278, 280, 282, 284, 286, 396, 398, 400
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OFFSET
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1,1
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COMMENTS
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LINKS
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MATHEMATICA
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r = Sqrt[6]; c = 1/2;
x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]
y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]
t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 500}];
Flatten[Position[t1, 1]] (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]] (* A194376 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194377 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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