A194423 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - <k*r>) = 0, where r=sqrt(2) and < > denotes fractional part.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 42, 45, 48, 54, 57, 60, 66, 69, 75, 78, 81, 87, 90, 93, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 141, 144, 147, 153, 156, 159, 165, 168, 171, 183, 195, 240, 243, 246, 252, 255, 258, 264

Offset

1,1

Comments

Every term is divisible by 3; see A194368.

Links

G. C. Greubel, Table of n, a(n) for n = 1..2043

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: A194416 A036686 A329926 * A059563 A292641 A085126

Adjacent sequences: A194420 A194421 A194422 * A194424 A194425 A194426

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved