A194393 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(13) and < > denotes fractional part.

2, 4, 6, 8, 24, 26, 28, 30, 32, 38, 40, 42, 44, 46, 62, 64, 66, 68, 70, 76, 78, 80, 82, 84, 100, 102, 104, 106, 108, 110, 112, 138, 140, 142, 144, 146, 148, 150, 176, 178, 180, 182, 184, 186, 188, 204, 206, 208, 210, 212, 218, 220, 222, 224, 226, 242, 244

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..57.

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, A194392, A194394.

Sequence in context: A029951 A062287 A189153 * A119260 A219616 A067732

Adjacent sequences: A194390 A194391 A194392 * A194394 A194395 A194396

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved