This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370278 #11 Mar 09 2024 11:42:04 %S A370278 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 A370278 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 A370278 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 A370278 Difference between the bound provided by Dirichlet's Simultaneous Approximation Theorem applied to Z_n (for d=3) and the best possible bound. %C A370278 Indices where this sequence is 0 form the sequence A370277. %C A370278 The indices of record high values form the sequence A370279. %e A370278 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 A370278 For example, consider the triple (1, 2, 3), with p = 2; we have: %e A370278 |2 * 1| mod 6 = 2, |2 * 2| mod 6 = 2, and |2 * 3| mod 6 = 0. %e A370278 Note that there is no nonzero choice of p such that all values are smaller than 2 for this triple. %Y A370278 Cf. A370277, A370279. %K A370278 nonn %O A370278 2,22 %A A370278 _Zachary DeStefano_, Feb 13 2024