A194402 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <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

1,1

Comments

Every term is even; see A194368 and A194403.

Links

Table of n, a(n) for n=1..61.

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 *)

Crossrefs

Cf. A001622, A194368, A194401, A194403, A194404.

Sequence in context: A234521 A085125 A251237 * A134930 A084562 A344453

Adjacent sequences: A194399 A194400 A194401 * A194403 A194404 A194405

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved