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A194415 Numbers n such that sum{<1/3+k*r>-<k*r> : 1<=k<=n}<0, where r=sqrt(3) and < > denotes fractional part. 5
1, 2, 4, 5, 8, 16, 17, 19, 20, 23, 31, 32, 34, 35, 38, 46, 47, 49, 50, 53, 56, 57, 58, 59, 60, 61, 62, 64, 65, 68, 71, 72, 73, 74, 75, 76, 77, 79, 80, 83, 86, 87, 88, 89, 90, 91, 92, 94, 95, 98, 101, 102, 103, 104, 105, 106, 107, 109, 110, 112, 113, 114, 115, 116 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..64.

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. A194368.

Sequence in context: A184775 A240075 A229083 * A160967 A045591 A045581

Adjacent sequences:  A194412 A194413 A194414 * A194416 A194417 A194418

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified December 17 18:04 EST 2014. Contains 252034 sequences.