A194387 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=sqrt(11) and < > denotes fractional part.

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 25, 27, 28, 29, 31, 47, 49, 50, 51, 53, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 85, 87, 88, 89, 91, 107, 109, 110, 111, 113, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 145, 147, 148, 149, 151, 167, 169, 170

Offset

1,1

Comments

See A194368.

Links

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

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, A194388, A194389.

Sequence in context: A008521 A299489 A039231 * A039175 A048293 A039129

Adjacent sequences: A194384 A194385 A194386 * A194388 A194389 A194390

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved