A194464 Numbers m such that Sum_{k=1..m} (<c + k*r> - <k*r>) > 0, where r=(1+sqrt(5))/2 and c=(1+sqrt(5))/4, and < > denotes fractional part.

5, 10, 13, 14, 15, 18, 19, 20, 26, 31, 34, 35, 36, 39, 40, 41, 47, 52, 68, 73, 89, 94, 99, 102, 103, 104, 107, 108, 109, 115, 120, 123, 124, 125, 128, 129, 130, 136, 141, 157, 162, 178, 183, 188, 191, 192, 193, 196, 197, 198, 204, 209, 212, 213, 214, 217

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..56.

Mathematica

r = GoldenRatio; c = FractionalPart[r/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]]    (* A184463 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]    (* A184464 *)

Crossrefs

Cf. A194368.

Sequence in context: A296445 A313376 A129846 * A192336 A001974 A242307

Adjacent sequences: A194461 A194462 A194463 * A194465 A194466 A194467

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved