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 A378872 #7 Dec 12 2024 09:25:19 %S A378872 5,8,5,13,12,12,5,20,21,8,40,21,40,40,5,29,32,60,17,60,85,85,96,32,17, %T A378872 85,96,17,96,96,5,40,45,24,104,13,148,148,165,24,148,8,221,148,12,221, %U A378872 260,45,104,148,165,148,221,12,260,104,165,221,260,165,260,260 %N A378872 Discriminant of the minimal polynomial of a number whose continued fraction expansion has periodic part given by the n-th composition (in standard order). %C A378872 Here, the minimal polynomial is required to have integer coefficients with no common divisors. %C A378872 If two numbers have eventually periodic continued fraction expansions with the same periodic part, the discriminants of their respective minimal polynomials are the same. %F A378872 a(n) = A378873(n)*A378874(n)^2. %F A378872 a(A059893(n)) = a(n), since reversing the periodic part of a continued fraction leaves the discriminant unchanged. %F A378872 a(A139706(n)) = a(n), since a circular shift of the periodic part of a continued fraction leaves the discriminant unchanged. %e A378872 For n = 6, the 5th composition is (1,2). The value of the continued fraction 1+1/(2+1/(1+1/(2+...))) is (1+sqrt(3))/2, whose minimal polynomial is 2*x^2-2*x-1 with discriminant a(6) = 12. %Y A378872 Cf. A059893, A066099 (compositions in standard order), A139706, A246903, A246921, A305311, A378873, A378874. %K A378872 nonn %O A378872 1,1 %A A378872 _Pontus von Brömssen_, Dec 10 2024