A370278 Difference between the bound provided by Dirichlet's Simultaneous Approximation Theorem applied to Z_n (for d=3) and the best possible bound.

0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3

Offset

2,22

Comments

Indices where this sequence is 0 form the sequence A370277.

The indices of record high values form the sequence A370279.

Links

Table of n, a(n) for n=2..118.

Example

For n = 6, floor(k^(2/3)) = 3, but for all triples (a_1, a_2, a_3), there is a choice of p such that |p*a_1| mod 6, |p*a_2| mod 6, and |p*a_3| mod 6 are all smaller than or equal to 2.
For example, consider the triple (1, 2, 3), with p = 2; we have:
|2 * 1| mod 6 = 2, |2 * 2| mod 6 = 2, and |2 * 3| mod 6 = 0.
Note that there is no nonzero choice of p such that all values are smaller than 2 for this triple.

Crossrefs

Cf. A370277, A370279.

Sequence in context: A283988 A276204 A365573 * A369245 A353310 A347883

Adjacent sequences: A370275 A370276 A370277 * A370279 A370280 A370281

Keyword

nonn

Author

Zachary DeStefano, Feb 13 2024

Status

approved