A194401 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) < 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.

1, 3, 9, 11, 17, 19, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 37, 43, 45, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 71, 77, 79, 85, 87, 111, 113, 119, 121, 145, 147, 153, 155, 161, 163, 165, 166, 167, 168, 169, 171, 173, 174, 175, 176, 177

Offset: 1

Author

Clark Kimberling, Aug 24 2011

Keywords

• nonn

Comments

See A194368.

Crossrefs

Cf. A001622, A194368, A194402, A194403, A194404.

Programs

Mathematica

r = GoldenRatio; c = 1/2;
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]]       (* A194401 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]       (* A194402 *)
%/2       (* A194403 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]       (* A194404 *)