A194420 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) = 0, where r=sqrt(5) and < > denotes fractional part.

3, 6, 9, 12, 21, 42, 60, 63, 72, 75, 78, 81, 84, 93, 114, 132, 135, 144, 147, 150, 153, 156, 165, 186, 204, 207, 216, 219, 222, 225, 228, 237, 258, 276, 279, 288, 291, 294, 297, 300, 309, 381, 453, 525, 597, 669, 687, 690

Offset

1,1

Comments

Every term is divisible by 3; see A194368.

Links

Table of n, a(n) for n=1..48.

Mathematica

r = Sqrt[5]; 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, 1000}];
Flatten[Position[t1, 1]]         (* A194419 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];
Flatten[Position[t2, 1]]         (* A194420 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]         (* A194421 *)

Crossrefs

Cf. A194368.

Sequence in context: A203016 A153838 A143829 * A367952 A277823 A233155

Adjacent sequences: A194417 A194418 A194419 * A194421 A194422 A194423

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved