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A194393
Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(13) and < > denotes fractional part.
4
2, 4, 6, 8, 24, 26, 28, 30, 32, 38, 40, 42, 44, 46, 62, 64, 66, 68, 70, 76, 78, 80, 82, 84, 100, 102, 104, 106, 108, 110, 112, 138, 140, 142, 144, 146, 148, 150, 176, 178, 180, 182, 184, 186, 188, 204, 206, 208, 210, 212, 218, 220, 222, 224, 226, 242, 244
OFFSET
1,1
COMMENTS
See A194368.
MATHEMATICA
r = Sqrt[13]; 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, 400}];
Flatten[Position[t1, 1]] (* A194392 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]] (* A194393 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194394 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 23 2011
STATUS
approved