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%I #28 Oct 27 2023 10:24:10
%S 1,5,3,4,1,5,7,7,4,4,9,1,4,2,6,6,9,1,5,4,3,5,9,7,0,0,7,6,1,0,9,3,7,5,
%T 7,0,1,8,8,2,5,4,5,0,3,8,5,1,6,5,9,5,1,3,5,3,6,8,5,3,1,8,6,3,0,0,8,0,
%U 6,3,0,2,3,2,1,4,0,8,2,2,8,1,4,3,6,7,8
%N Decimal expansion of real root of x^5 - x^3 - x^2 - x - 1.
%C This root is also the sixth smallest of the Pisot numbers.
%H Iain Fox, <a href="/A293509/b293509.txt">Table of n, a(n) for n = 1..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_number">Pisot-Vijayaraghavan number</a>
%H <a href="/index/Al#algebraic_05">Index entries for algebraic numbers, degree 5</a>
%e 1.53415774491426691543597007610937570188254503851659513536853186300806302321...
%t RealDigits[ Solve[ x^5 - x^3 - x^2 - x - 1 == 0, x, WorkingPrecision -> 111][[-1, 1, 2]], 10, 111][[1]] (* _Robert G. Wilson v_, Nov 04 2017 *)
%o (PARI) solve(x=1, 2, x^5 - x^3 - x^2 - x - 1) \\ _Michel Marcus_, Oct 13 2017
%o (PARI) default(realprecision, 20080); x=solve(x=1, 2, x^5 - x^3 - x^2 - x - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b293509.txt", n, " ", d)); \\ _Iain Fox_, Oct 23 2017
%o (PARI) polrootsreal(x^5 - x^3 - x^2 - x - 1)[1] \\ _Charles R Greathouse IV_, Nov 04 2017
%Y Cf. A060006, A086106, A228777, A092526, A293506, A293508, A293557.
%K cons,nonn
%O 1,2
%A _Iain Fox_, Oct 11 2017