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A194418
Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(3) and < > denotes fractional part.
5
7, 10, 11, 13, 14, 22, 25, 26, 28, 29, 37, 40, 41, 43, 44, 52, 55, 67, 70, 82, 85, 97, 100, 160, 163, 164, 166, 167, 175, 178, 179, 181, 182, 190, 193, 194, 196, 197, 205, 208, 220, 223, 235, 238, 250, 253, 373, 376, 388, 391, 403, 406
OFFSET
1,1
COMMENTS
See A194368.
MATHEMATICA
r = Sqrt[3]; 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, 150}];
Flatten[Position[t1, 1]] (* A194415 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]] (* A194416 *)
%/3 (* A194417 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 500}];
Flatten[Position[t3, 1]] (* A194418 *)
CROSSREFS
Cf. A194368.
Sequence in context: A060228 A190231 A191875 * A094764 A066468 A347393
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 24 2011
STATUS
approved