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A194418 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(3) and < > denotes fractional part. 5
7, 10, 11, 13, 14, 22, 25, 26, 28, 29, 37, 40, 41, 43, 44, 52, 55, 67, 70, 82, 85, 97, 100, 160, 163, 164, 166, 167, 175, 178, 179, 181, 182, 190, 193, 194, 196, 197, 205, 208, 220, 223, 235, 238, 250, 253, 373, 376, 388, 391, 403, 406 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A194368.

LINKS

Table of n, a(n) for n=1..52.

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: A060228 A190231 A191875 * A094764 A066468 A347393

Adjacent sequences:  A194415 A194416 A194417 * A194419 A194420 A194421

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified January 18 00:50 EST 2022. Contains 350410 sequences. (Running on oeis4.)