A194392 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(13) and < > denotes fractional part.

1, 3, 29, 31, 33, 34, 35, 36, 37, 39, 41, 67, 69, 71, 72, 73, 74, 75, 77, 79, 105, 107, 143, 145, 181, 183, 209, 211, 213, 214, 215, 216, 217, 219, 221, 247, 249, 251, 252, 253, 254, 255, 257, 259, 285, 287, 323, 325, 361, 363, 389, 391, 393, 394, 395

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..55.

Mathematica

r = Sqrt[13]; 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, 400}];
Flatten[Position[t1, 1]]       (* A194392 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]       (* A194393 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]       (* A194394 *)

Crossrefs

Cf. A010470, A194368, A194393, A194394.

Sequence in context: A292625 A030274 A249518 * A189571 A055062 A086174

Adjacent sequences: A194389 A194390 A194391 * A194393 A194394 A194395

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved