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%I #11 Mar 09 2024 11:42:04
%S 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,
%T 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,
%U 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
%N Difference between the bound provided by Dirichlet's Simultaneous Approximation Theorem applied to Z_n (for d=3) and the best possible bound.
%C Indices where this sequence is 0 form the sequence A370277.
%C The indices of record high values form the sequence A370279.
%e 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.
%e For example, consider the triple (1, 2, 3), with p = 2; we have:
%e |2 * 1| mod 6 = 2, |2 * 2| mod 6 = 2, and |2 * 3| mod 6 = 0.
%e Note that there is no nonzero choice of p such that all values are smaller than 2 for this triple.
%Y Cf. A370277, A370279.
%K nonn
%O 2,22
%A _Zachary DeStefano_, Feb 13 2024
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