A194419 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) < 0, where r=sqrt(5) and < > denotes fractional part.

4, 5, 8, 59, 76, 77, 80, 131, 148, 149, 152, 203, 220, 221, 224, 275, 292, 293, 296, 686, 758, 830, 902, 974, 991, 992, 995

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..27.

Mathematica

r = Sqrt[5]; c = 1/3;
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, 1000}];
Flatten[Position[t1, 1]]         (* A194419 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];
Flatten[Position[t2, 1]]         (* A194420 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]         (* A194421 *)

Crossrefs

Cf. A194368.

Sequence in context: A229861 A140315 A055497 * A175380 A263151 A366185

Adjacent sequences: A194416 A194417 A194418 * A194420 A194421 A194422

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved