A194401 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.

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

1,2

Comments

See A194368.

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, A194402, A194403, A194404.

Sequence in context: A310316 A096187 A310317 * A190238 A047471 A354938

Adjacent sequences: A194398 A194399 A194400 * A194402 A194403 A194404

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved