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 A383067 #6 Apr 19 2025 06:16:07 %S A383067 1,2,3,4,5,7,19,22 %N A383067 The set of positive integers k which can be expressed as a sum of two units in some cyclic cubic field. %C A383067 These are all the positive integers k such that there exists some cubic number field K whose Galois group is cyclic (C_3) and contains units u, v in K such that k = u + v. %H A383067 M. Tinková, R. Visser, and P. Yatsyna, <a href="https://arxiv.org/abs/2502.01345">Sums of two units in number fields</a>, arXiv:2502.01345 [math.NT], 2025. %H A383067 I. Vukusic and V. Ziegler, <a href="https://doi.org/10.5802/jtnb.1223">On a family of unit equations over simplest cubic fields</a>, J. Théor. Nombres Bordeaux 34 (2022), no. 3, 705-718. %e A383067 For each positive integer k given in the sequence, it can be written as a sum of two units in some cyclic cubic field as follows: %e A383067 1 = u + (-u+1), where u is a root of x^3 + x^2 - 2x - 1. %e A383067 2 = u + (-u+2), where u is a root of x^3 - 3x - 1. %e A383067 3 = (u^2) + (-u^2+3), where u is a root of x^3 + x^2 - 2x - 1. %e A383067 4 = (u^2+2u) + (-u^2-2u+4), where u is a root of x^3 + x^2 - 2x - 1. %e A383067 5 = (u^2-u) + (-u^2+u+5), where u is a root of x^3 + x^2 - 2x - 1. %e A383067 7 = (u^2) + (-u^2+7), where u is a root of x^3 - x^2 - 4x - 1. %e A383067 19 = (5u^2+9u) + (-5u^2-9u+19), where u is a root of x^3 + x^2 - 2x - 1. %e A383067 22 = (4u^2-5u) + (-4u^2+5u+22), where u is a root of x^3 + x^2 - 2x - 1. %Y A383067 Cf. A383068. %K A383067 nonn,fini,full %O A383067 1,2 %A A383067 _Robin Visser_, Apr 15 2025