A194404 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.

5, 7, 13, 15, 39, 41, 47, 49, 73, 75, 81, 83, 89, 91, 93, 94, 95, 96, 97, 99, 101, 102, 103, 104, 105, 107, 109, 115, 117, 123, 125, 127, 128, 129, 130, 131, 133, 135, 136, 137, 138, 139, 141, 143, 149, 151, 157, 159, 183, 185, 191, 193, 217, 219, 225

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..55.

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, A194402, A194403.

Sequence in context: A314316 A314317 A314318 * A064465 A314319 A314320

Adjacent sequences: A194401 A194402 A194403 * A194405 A194406 A194407

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved