A194392 Numbers m such that Sum_{k=1..m} (<1/2 + 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

Author

Clark Kimberling, Aug 23 2011

Keywords

• nonn

Comments

See A194368.

Crossrefs

Cf. A010470, A194368, A194393, A194394.

Programs

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 *)