A194425 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - <k*r>) > 0, where r=sqrt(2) and < > denotes fractional part.

5, 8, 10, 11, 17, 20, 22, 23, 29, 32, 34, 35, 37, 38, 39, 40, 41, 44, 46, 47, 49, 50, 51, 52, 53, 56, 58, 59, 61, 62, 63, 64, 65, 68, 80, 92, 104, 107, 109, 110, 116, 119, 121, 122, 128, 131, 133, 134, 136, 137, 138, 139, 140, 143, 145, 146, 148, 149, 150

Offset

1,1

Comments

See A194368.

Links

G. C. Greubel, Table of n, a(n) for n = 1..2230

Mathematica

r = Sqrt[2]; c = 2/3;
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, 300}];
Flatten[Position[t1, 1]]         (* A194422 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]         (* A194423 *)
%/3         (* A194424 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]         (* A194425 *)

Crossrefs

Cf. A194368.

Sequence in context: A156288 A270535 A287110 * A314376 A205841 A344443

Adjacent sequences: A194422 A194423 A194424 * A194426 A194427 A194428

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved