A194382 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(8) and < > denotes fractional part.

4, 6, 10, 12, 16, 18, 22, 24, 28, 30, 34, 40, 46, 52, 58, 64, 104, 110, 116, 122, 128, 134, 138, 140, 144, 146, 150, 152, 156, 158, 162, 164, 168, 170, 172, 176, 178, 182, 184, 188, 190, 194, 196, 200, 202, 204, 208, 210, 214, 216, 220, 222, 226, 228

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..54.

Mathematica

r = Sqrt[8]; 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, 100}];
Flatten[Position[t1, 1]]   (* A194381 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]   (* A194382 *)
%/2  (* A194383 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
Flatten[Position[t3, 1]]   (* A194384 *)

Crossrefs

Cf. A010466, A194368, A194383.

Sequence in context: A166986 A318487 A047233 * A296655 A310577 A353465

Adjacent sequences: A194379 A194380 A194381 * A194383 A194384 A194385

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved