A194380 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(7) and < > denotes fractional part.

31, 33, 45, 47, 79, 81, 93, 95, 127, 129, 141, 143, 175, 177, 189, 191, 223, 225, 237, 239, 525, 527, 539, 541, 573, 575, 587, 589, 621, 623, 635, 637, 669, 671, 683, 685, 717, 719, 731, 733

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..40.

Mathematica

r = Sqrt[7]; 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]]   (* A194378 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]  (* A194379 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 800}];
Flatten[Position[t3, 1]]   (* A194380 *)

Crossrefs

Cf. A194368, A194378, A194379.

Sequence in context: A280647 A152045 A041479 * A269267 A361263 A025358

Adjacent sequences: A194377 A194378 A194379 * A194381 A194382 A194383

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved