A194416 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) = 0, where r=sqrt(3) and < > denotes fractional part.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 63, 66, 69, 78, 81, 84, 93, 96, 99, 108, 111, 123, 126, 138, 141, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 216, 219, 222, 231, 234

Offset

1,1

Comments

Every term is divisible by 3; see A194368.

Links

Table of n, a(n) for n=1..57.

Mathematica

r = Sqrt[3]; 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, 150}];
Flatten[Position[t1, 1]]           (* A194415 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]           (* A194416 *)
%/3                                (* A194417 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 500}];
Flatten[Position[t3, 1]]           (* A194418 *)

Crossrefs

Cf. A002194, A194368, A194415, A194417, A194418.

Sequence in context: A008585 A008486 A135943 * A036686 A329926 A194423

Adjacent sequences: A194413 A194414 A194415 * A194417 A194418 A194419

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved