cp's OEIS Frontend

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.

A103546 Decimal expansion of the negated value of the smallest real root of the quintic equation x^5 + 2*x^4 - 2*x^3 - x^2 + 2*x -1 = 0.

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%I A103546 #19 Feb 16 2025 08:32:56
%S A103546 2,4,8,6,3,4,3,7,6,4,9,5,9,0,7,9,6,6,5,2,6,7,1,9,5,3,3,0,9,7,0,7,2,2,
%T A103546 1,2,0,1,4,0,9,0,3,8,5,2,5,9,2,7,0,5,8,1,9,7,6,4,9,9,4,0,3,3,2,9,9,1,
%U A103546 1,1,8,5,4,0,0,1,1,4,7,3,0,5,5,1,5,5,9,0,9,1,0,4,6,9,2,8,0,8,0,1,7,2,3,1,7
%N A103546 Decimal expansion of the negated value of the smallest real root of the quintic equation x^5 + 2*x^4 - 2*x^3 - x^2 + 2*x -1 = 0.
%C A103546 This is an approximation to the Feigenbaum reduction parameter.
%C A103546 The other two real roots are 0.76660865407289... and -1.16317291980104...
%H A103546 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FeigenbaumConstant.html">Feigenbaum Constant</a>.
%H A103546 <a href="/index/Al#algebraic_05">Index entries for algebraic numbers, degree 5</a>
%e A103546 The real roots are (roughly) -2.486343765, -1.163172920, 0.7666086541.
%t A103546 RealDigits[ FindRoot[x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1 == 0, {x, -3}, WorkingPrecision -> 2^7][[1, 2]]][[1]] (* _Robert G. Wilson v_, Mar 26 2005 *)
%t A103546 Root[#^5 + 2#^4 - 2#^3 - #^2 + 2# - 1&, 1] // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 27 2013 *)
%o A103546 (PARI) polrootsreal(x^5 - 2*x^4 - 2*x^3 + x^2 + 2*x + 1)[3] \\ _Charles R Greathouse IV_, Apr 14 2014
%Y A103546 Cf. A006891, A103616.
%K A103546 cons,nonn
%O A103546 1,1
%A A103546 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Mar 23 2005