A194466 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) > 0, where r=sqrt(2) and c=sqrt(1/2), and < > denotes fractional part.

3, 5, 6, 10, 17, 20, 22, 23, 27, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 44, 46, 47, 51, 58, 61, 63, 64, 68, 75, 92, 99, 102, 104, 105, 109, 116, 119, 121, 122, 126, 128, 129, 131, 132, 133, 134, 135, 136, 138, 139, 143, 145, 146, 150, 157, 160, 162, 163

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..58.

Mathematica

r = Sqrt[2]; 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]]    (* A184465 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]    (* A184466 *)

Crossrefs

Cf. A194368.

Sequence in context: A238488 A230124 A027627 * A270416 A290269 A115059

Adjacent sequences: A194463 A194464 A194465 * A194467 A194468 A194469

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved