A194421 Numbers m such that Sum_{k=1..m} (<1/3 + k*r> - <k*r>) > 0, where r=sqrt(5) and < > denotes fractional part.

1, 2, 7, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 79, 82, 83, 85, 86, 87

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..67.

Mathematica

r = Sqrt[5]; c = 1/3;
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, 1000}];
Flatten[Position[t1, 1]]         (* A194419 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 700}];
Flatten[Position[t2, 1]]         (* A194420 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]         (* A194421 *)

Crossrefs

Cf. A194368.

Sequence in context: A236243 A024831 A362861 * A043357 A023730 A045281

Adjacent sequences: A194418 A194419 A194420 * A194422 A194423 A194424

Keyword

nonn

Author

Clark Kimberling, Aug 24 2011

Status

approved