A194389 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(11) and < > denotes fractional part.

1, 17, 19, 20, 21, 23, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 55, 57, 58, 59, 61, 77, 79, 80, 81, 83, 93, 95, 96, 97, 98, 99, 100, 101, 102, 103, 105, 115, 117, 118, 119, 121, 137, 139, 140, 141, 143, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..58.

Mathematica

r = Sqrt[11]; 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]]     (* A194387 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]     (* A194388 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]     (* A194389 *)

Crossrefs

Cf. A010468, A194368, A194387, A194388.

Sequence in context: A042399 A156656 A130808 * A030127 A115849 A230634

Adjacent sequences: A194386 A194387 A194388 * A194390 A194391 A194392

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved