A194462 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.

1, 2, 4, 5, 7, 10, 13, 14, 15, 17, 18, 20, 23, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 59, 60, 62, 65, 68, 69, 70, 72, 73, 75, 78, 81, 82, 83, 85, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 98, 99, 101

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..68.

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: A058212 A007997 A123120 * A163267 A036559 A083022

Adjacent sequences: A194459 A194460 A194461 * A194463 A194464 A194465

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved