A194399 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(15) and < > denotes fractional part.

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

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