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 A370277 #20 Mar 09 2024 11:41:09 %S A370277 2,4,5,7,8,10,11,14,18,26,27,30,31,63,64,68,69,70,76,124,125,130,131, %T A370277 132,148,215,216,222,223,224,225,234,342,343,350,351,352,353 %N A370277 Numbers k with the property that Dirichlet's Simultaneous Approximation Theorem applied to Z_k is tight (for d = 3). %C A370277 Dirichlet's Simultaneous Approximation Theorem applied to Z_k states that for all a_1, a_2, ..., a_d, there exists a nonzero p such that |pa_i| <= k^(1 - 1/d) mod k. %C A370277 For d = 3, the bound of floor(k^(2/3)) is tight only for specific values of k. That is to say, max_(a_1,a_2,a_3) min_p max_i |pa_i| = floor(k^(2/3)) only for specific values of k. These are those values. %C A370277 This sequence consists of the indices of the zeros in A370278. %C A370277 It appears that this sequence contains all integers k such that k or k+1 is a cube. %H A370277 Stack Exchange <a href="https://math.stackexchange.com/questions/4862334/tighten-corollary-of-dirichlets-simultaneous-approximation-bound-d-3">Dirichlet's Simultaneous Approximation Bound</a>. %e A370277 For k = 14, floor(k^(2/3)) = 5. Given the triple (1, 3, 5), there is no choice of p such that |p| mod 14, |3p| mod 14, and |5p| mod 14 are all smaller than 5. %e A370277 p = 1, 3, 5, 9, 11, and 13 results in a simultaneous minimum of 5. %Y A370277 Cf. A370278, A370279. %K A370277 nonn,more %O A370277 1,1 %A A370277 _Zachary DeStefano_, Feb 13 2024