A194412 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) = 0, where r=sqrt(2) and < > denotes fractional part.

3, 9, 12, 15, 21, 24, 27, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 75, 78, 81, 87, 90, 93, 99, 102, 108, 111, 114, 120, 123, 126, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 183, 195, 207, 210, 213, 219, 222, 225, 231

Offset

1,1

Comments

Every term is a multiple of 3; see A194368.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

r = Sqrt[2]; c = 1/3;
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, 200}];
Flatten[Position[t1, 1]]         (* A194411 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 400}];
Flatten[Position[t2, 1]]         (* A194412 *)
%/3                              (* A194413 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 150}];
Flatten[Position[t3, 1]]         (* A194414 *)

Crossrefs

Cf. A002193, A194368, A194411, A194413, A194414.

Sequence in context: A089425 A255686 A138921 * A136290 A244147 A103531

Adjacent sequences: A194409 A194410 A194411 * A194413 A194414 A194415

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved