A194396 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(14) and < > denotes fractional part.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 34, 38, 42, 46, 50, 54, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 94, 98, 102, 106, 110, 114, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150

Offset

1,1

Comments

Every term is even; see A194368.

Links

Table of n, a(n) for n=1..61.

Mathematica

r = Sqrt[14]; 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, 200}];
Flatten[Position[t1, 1]]       (* A194395 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194396 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t3, 1]]       (* A194397 *)

Crossrefs

Cf. A010471, A194368, A194395, A194397.

Sequence in context: A368861 A141098 A084563 * A321193 A284788 A323288

Adjacent sequences: A194393 A194394 A194395 * A194397 A194398 A194399

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved