A194461 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) < 0, where r=(1+sqrt(5))/2 and c=(-1+sqrt(5))/4, and < > denotes fractional part.

3, 6, 8, 9, 11, 12, 16, 19, 21, 22, 24, 25, 29, 32, 42, 45, 55, 58, 61, 63, 64, 66, 67, 71, 74, 76, 77, 79, 80, 84, 87, 97, 100, 110, 113, 116, 118, 119, 121, 122, 126, 129, 131, 132, 134, 135, 139, 142, 144, 145, 147, 148, 150, 151, 152, 153, 154, 155, 156

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..59.

Mathematica

r = GoldenRatio; c = (1/2) FractionalPart[r];
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]]  (* A184461 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]  (* A184462 *)

Crossrefs

Cf. A194368.

Sequence in context: A190234 A036558 A005870 * A186385 A335155 A231005

Adjacent sequences: A194458 A194459 A194460 * A194462 A194463 A194464

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved