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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 09:54 EST 2021. Contains 349419 sequences. (Running on oeis4.)