

A194420


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


4



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
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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 * A277823 A233155 A118519
Adjacent sequences: A194417 A194418 A194419 * A194421 A194422 A194423


KEYWORD

nonn


AUTHOR

Clark Kimberling, Aug 24 2011


STATUS

approved



