A194384 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(8) and < > denotes fractional part.

5, 11, 17, 23, 29, 139, 145, 151, 157, 163, 169, 173, 174, 175, 179, 180, 181, 185, 186, 187, 191, 192, 193, 197, 198, 199, 203, 209, 215, 221, 227, 233, 343, 349, 355, 361, 367, 373, 377, 378, 379, 383, 384, 385, 389, 390, 391, 395, 396, 397, 401

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..51.

Mathematica

r = Sqrt[8]; 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]]   (* A194381 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]   (* A194382 *)
%/2  (* A194383 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 600}];
Flatten[Position[t3, 1]]   (* A194384 *)

Crossrefs

Cf. A010466, A194368, A194381, A194382, A194383.

Sequence in context: A181575 A335070 A354748 * A287305 A189938 A184525

Adjacent sequences: A194381 A194382 A194383 * A194385 A194386 A194387

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved