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 A261882 #38 May 07 2024 05:35:49
%S A261882 1,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,
%T A261882 1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5,1,8,5
%N A261882 Decimal expansion of 32/27.
%C A261882 For any number x >= 32/27 and any e > 0, there is a graph G such that the chromatic polynomial of G has a real root between x - e and x + e. (All real roots of such polynomials are 0, 1, or in this range.)
%C A261882 Continued fraction expansion of (sqrt(730)-10)/9. - _Bruno Berselli_, Sep 04 2015
%C A261882 Periodic (beyond the first term) with period 3. - _Charles R Greathouse IV_, Sep 05 2015
%C A261882 Equals the ratio of the wavelengths between the hydrogen spectral lines Lyman-alpha (121.6 nm) and Lyman-beta (102.6 nm). - _Sean Stroud_, Apr 15 2019
%H A261882 Peter J. Cameron's Blog, <a href="https://cameroncounts.wordpress.com/2016/10/04/algebraic-properties-of-chromatic-roots/">Algebraic properties of chromatic roots</a>, Oct 04 2016.
%H A261882 Bill Jackson, <a href="http://dx.doi.org/10.1017/S0963548300000705">A zero-free interval for chromatic polynomials of graphs</a>, Combinatorics, Probability and Computing 2:3 (Sept 1993), pp. 325-336.
%H A261882 Bill Jackson and Alan Sokal, <a href="http://dx.doi.org/10.1016/j.jctb.2009.03.002">Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and matroids</a>, J. Combin. Theory Ser. B 99:6 (2009), pp. 869-903.
%H A261882 Carsten Thomassen, <a href="https://doi.org/10.1017/S0963548397003131">The zero-free intervals for chromatic polynomials of graphs</a>, Combin. Probab. Comput. 6:4 (1997), pp. 497-506.
%H A261882 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1).
%F A261882 G.f.: x*(1 + x + 8*x^2 + 4*x^3)/((1 - x)*(1 + x + x^2)). - _Bruno Berselli_, Sep 04 2015
%F A261882 a(n) = 7-(-1)^(n-1 mod 3)/2-5*(-1)^(n mod 3)/2-4*(-1)^(n+1 mod 3), n>1. - _Wesley Ivan Hurt_, Sep 04 2015
%e A261882 1.18518518518518518...
%p A261882 Digits := 100; evalf(32/27); # _Wesley Ivan Hurt_, Sep 04 2015
%t A261882 First@ RealDigits[N[32/27, 120]] (* _Michael De Vlieger_, Sep 04 2015 *)
%t A261882 Join[{1}, Table[7 - (-1)^Mod[n - 1, 3]/2 - 5 (-1)^Mod[n, 3]/2 - 4 (-1)^Mod[n + 1, 3], {n, 2, 40}]] (* _Wesley Ivan Hurt_, Sep 04 2015 *)
%o A261882 (PARI) 32/27.
%Y A261882 Cf. A021058.
%K A261882 nonn,cons,easy
%O A261882 1,3
%A A261882 _Charles R Greathouse IV_, Sep 04 2015