A194391 Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(12) and < > denotes fractional part.

1, 3, 5, 7, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 31, 33, 35, 37, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 59, 61, 63, 65, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 87, 89, 91, 93

Offset

1,2

Comments

See A194368.

Links

Table of n, a(n) for n=1..68.

Mathematica

r = Sqrt[12]; 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]]  (* empty *)
t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];
Flatten[Position[t2, 1]]       (* A194390 *)
t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 100}];
Flatten[Position[t3, 1]]       (* A194391 *)

Crossrefs

Cf. A010469, A194368, A194390.

Sequence in context: A082655 A050828 A329405 * A347468 A081534 A214547

Adjacent sequences: A194388 A194389 A194390 * A194392 A194393 A194394

Keyword

nonn

Author

Clark Kimberling, Aug 23 2011

Status

approved