A194388 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(11) and < > denotes fractional part.

2, 4, 14, 16, 18, 22, 24, 26, 30, 32, 34, 44, 46, 48, 52, 54, 56, 60, 62, 64, 74, 76, 78, 82, 84, 86, 90, 92, 94, 104, 106, 108, 112, 114, 116, 120, 122, 124, 134, 136, 138, 142, 144, 146, 150, 152, 154, 164, 166, 168, 172, 174, 176, 180, 182, 184, 194, 196

Offset

1,1

Comments

Every term is even; see A194368.

Links

Table of n, a(n) for n=1..58.

Mathematica

r = Sqrt[11]; 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]]     (* A194387 *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t2, 1]]     (* A194388 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 200}];
Flatten[Position[t3, 1]]     (* A194389 *)

Crossrefs

Cf. A010468, A194368, A194387, A194389.

Sequence in context: A095909 A151872 A087420 * A141654 A173338 A054600

Adjacent sequences: A194385 A194386 A194387 * A194389 A194390 A194391

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved