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A194416 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) = 0, where r=sqrt(3) and < > denotes fractional part. 5
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 (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..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

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Last modified November 27 07:28 EST 2021. Contains 349365 sequences. (Running on oeis4.)