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A194399 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(15) and < > denotes fractional part. 4
6, 8, 14, 16, 22, 24, 30, 32, 38, 40, 46, 48, 54, 56, 62, 70, 78, 86, 94, 102, 110, 118, 314, 322, 330, 338, 346, 354, 362, 370, 376, 378, 384, 386, 392, 394, 400, 402, 408, 410, 416, 418, 424, 426, 432, 434, 438, 442, 446, 450, 454, 458, 462, 466, 470 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every term is even; see A194368.

LINKS

Table of n, a(n) for n=1..55.

MATHEMATICA

r = Sqrt[15]; c = 1/2;

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, 100}];

Flatten[Position[t1, 1]]       (* A194398 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 800}];

Flatten[Position[t2, 1]]       (* A194399 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];

Flatten[Position[t3, 1]]       (* A194400 *)

CROSSREFS

Cf. A010472, A194368, A194398, A194400.

Sequence in context: A315884 A178950 A047451 * A315885 A315886 A315887

Adjacent sequences:  A194396 A194397 A194398 * A194400 A194401 A194402

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified September 22 17:39 EDT 2021. Contains 347607 sequences. (Running on oeis4.)