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A194419
Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) < 0, where r=sqrt(5) and < > denotes fractional part.
4
4, 5, 8, 59, 76, 77, 80, 131, 148, 149, 152, 203, 220, 221, 224, 275, 292, 293, 296, 686, 758, 830, 902, 974, 991, 992, 995
OFFSET
1,1
COMMENTS
See A194368.
MATHEMATICA
r = Sqrt[5]; c = 1/3;
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, 1000}];
Flatten[Position[t1, 1]] (* A194419 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];
Flatten[Position[t2, 1]] (* A194420 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]] (* A194421 *)
CROSSREFS
Cf. A194368.
Sequence in context: A229861 A140315 A055497 * A175380 A263151 A366185
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 24 2011
STATUS
approved