A194402 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - ) = 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 26, 28, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 60, 62, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 98, 100, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 132, 134, 140, 142, 144, 146, 148, 150, 152, 154

Offset: 1

Author

Clark Kimberling, Aug 24 2011

Keywords

• nonn

Comments

Every term is even; see A194368 and A194403.

Crossrefs

Cf. A001622, A194368, A194401, 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 *)