A194467 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) < 0, where r=sqrt(3) and c=sqrt(1/3), and < > denotes fractional part.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..69.

Mathematica

Remove["Global`*"];
r = Sqrt[3]; c = 1/r;
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]]    (* A184467 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 900}];
Flatten[Position[t3, 1]]    (* A184468 *)

Crossrefs

Cf. A194368.

Sequence in context: A071959 A176845 A196127 * A225857 A168134 A245030

Adjacent sequences: A194464 A194465 A194466 * A194468 A194469 A194470

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved