A194419 Numbers m such that Sum_{k=1..m} (<1/3 + 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

Author

Clark Kimberling, Aug 24 2011

Keywords

• nonn

Comments

See A194368.

Crossrefs

Cf. A194368.

Programs

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 *)