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 A257945 #15 Aug 21 2023 11:42:24 %S A257945 6,9,3,2,0,5,4,6,4,6,2,3,7,9,7,3,2,0,4,3,4,3,6,3,7,0,4,2,2,4,1,3,8,6, %T A257945 8,7,9,4,1,0,2,1,7,5,0,1,6,9,2,1,9,0,1,3,3,9,9,5,5,5,8,6,7,5,2,9,5,5, %U A257945 8,1,4,8,8,3,1,6,6,1,0,4,3,0,2,2,3,3,6,0,6,9,1,5,2,6,8,1,8,5,8,3,5,0,5,6,4 %N A257945 Decimal expansion of abs(i/(i + i/(i + i/...))) and abs(i/(1 + i/(1 + i/...))), i being the imaginary unit. %C A257945 Set v = A156590 and u = (A156548 - 1). Then the continued fractions evaluate to i/(i + i/(i + i/...)) = (sqrt(4*i - 1) - i)/2 = v + u*i and i/(1 + i/(1 + i/...)) = (sqrt(4*i + 1) - 1)/2 = u + v*i. They can be evaluated either explicitly or as limits of the convergent recursive mappings z -> i/(i + z) and z -> i/(1 + z), respectively, starting, for example, with z = 0. %C A257945 An algebraic integer of degree 8. - _Charles R Greathouse IV_, Jun 02 2015 %H A257945 Stanislav Sykora, <a href="/A257945/b257945.txt">Table of n, a(n) for n = 0..2000</a> %H A257945 <a href="/index/Al#algebraic_08">Index entries for algebraic numbers, degree 8</a> %F A257945 Equals sqrt(1 + sqrt(17) - sqrt(2*(1 + sqrt(17))))/2. %e A257945 0.69320546462379732043436370422413868794102175016921901339955586752... %t A257945 RealDigits[Sqrt[1 + Sqrt[17] - Sqrt[2*(1 + Sqrt[17])]]/2, 10, 105][[1]] (* _Vaclav Kotesovec_, Jun 02 2015 *) %o A257945 (PARI) sqrt(1+sqrt(17)-sqrt(2*(1+sqrt(17))))/2 %o A257945 (PARI) polrootsreal(x^8-x^6-2*x^4-x^2+1)[3] \\ _Charles R Greathouse IV_, Jun 02 2015 %Y A257945 Cf. A156548, A156590. %K A257945 nonn,cons %O A257945 0,1 %A A257945 _Stanislav Sykora_, May 29 2015