A194463 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, 3, 4, 6, 7, 8, 9, 11, 12, 16, 17, 21, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 37, 38, 42, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..69.

Mathematica

r = GoldenRatio; c = FractionalPart[r/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]]    (* A184463 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]    (* A184464 *)

Crossrefs

Cf. A194368.

Sequence in context: A336654 A004436 A028237 * A140467 A103677 A087919

Adjacent sequences: A194460 A194461 A194462 * A194464 A194465 A194466

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved