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A194388
Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(11) and < > denotes fractional part.
4
2, 4, 14, 16, 18, 22, 24, 26, 30, 32, 34, 44, 46, 48, 52, 54, 56, 60, 62, 64, 74, 76, 78, 82, 84, 86, 90, 92, 94, 104, 106, 108, 112, 114, 116, 120, 122, 124, 134, 136, 138, 142, 144, 146, 150, 152, 154, 164, 166, 168, 172, 174, 176, 180, 182, 184, 194, 196
OFFSET
1,1
COMMENTS
Every term is even; see A194368.
MATHEMATICA
r = Sqrt[11]; 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, 200}];
Flatten[Position[t1, 1]] (* A194387 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]] (* A194388 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]] (* A194389 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 23 2011
STATUS
approved