A194418 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(3) and < > denotes fractional part.

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.

Links

Table of n, a(n) for n=1..52.

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

Adjacent sequences: A194415 A194416 A194417 * A194419 A194420 A194421

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved