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A370278
Difference between the bound provided by Dirichlet's Simultaneous Approximation Theorem applied to Z_n (for d=3) and the best possible bound.
2
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.
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
Sequence in context: A283988 A276204 A365573 * A369245 A353310 A347883
KEYWORD
nonn
AUTHOR
Zachary DeStefano, Feb 13 2024
STATUS
approved