A194394 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(13) and < > denotes fractional part.

5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 43, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 65, 81, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 101, 103, 109, 111, 113, 114, 115, 116, 117

Offset

1,1

Comments

See A194368.

Links

Table of n, a(n) for n=1..64.

Mathematica

r = Sqrt[13]; 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, 400}];
Flatten[Position[t1, 1]]       (* A194392 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]       (* A194393 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]       (* A194394 *)

Crossrefs

Cf. A010470, A194368, A194392, A194393.

Sequence in context: A364681 A143730 A354454 * A160811 A116451 A126949

Adjacent sequences: A194391 A194392 A194393 * A194395 A194396 A194397

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved