A160155 - OEIS

%I #25 Aug 21 2023 10:20:06

%S 1,1,6,7,3,0,3,9,7,8,2,6,1,4,1,8,6,8,4,2,5,6,0,4,5,8,9,9,8,5,4,8,4,2,

%T 1,8,0,7,2,0,5,6,0,3,7,1,5,2,5,4,8,9,0,3,9,1,4,0,0,8,2,4,4,9,2,7,5,6,

%U 5,1,9,0,3,4,2,9,5,2,7,0,5,3,1,8,0,6,8,5,2,0,5,0,4,9,7,2,8,6,7,2,8,9,5,3,5

%N Decimal expansion of the one real root of x^5-x-1.

%C The other (complex) roots are 0.181232444469875383... + 1.08395410131771066...*i, and -0.764884433600584726... + 0.352471546031726249...*i, together with their complex conjugates. - _Wolfdieter Lang_, Dec 15 2022

%H Harry J. Smith, <a href="/A160155/b160155.txt">Table of n, a(n) for n = 1..20000</a>

%H David W. Boys, <a href="http://dx.doi.org/10.1090/S0025-5718-1985-0790657-8">The maximal modulus of an algebraic integer</a>, Math. Comp. 45 (1985) 243-249, table page S18.

%H Qiang Wu, <a href="http://dx.doi.org/10.1090/S0025-5718-10-02345-8">The smallest Perron numbers</a>, Math. Comp. 79 (2010) 2387-2394

%H <a href="/index/Al#algebraic_05">Index entries for algebraic numbers, degree 5</a>

%F Equals (1 + (1 + (1 + (1 + (1 + ...)^(1/5))^(1/5))^(1/5))^(1/5))^(1/5). - _Ilya Gutkovskiy_, Dec 15 2017

%e 1.16730397826141868425604589985484218072056037152548903914008244927565...

%t RealDigits[Root[x^5-x-1, x, 1], 10, 105] // First (* _Jean-François Alcover_, Jul 09 2015 *)

%o (PARI)  default(realprecision, 20080); x=NULL; p=x^5 - x - 1; rs=polroots(p); r=real(rs[1]); for (n=1, 20000, d=floor(r); r=(r-d)*10; write("b160155.txt", n, " ", d));

%o (PARI) polrootsreal(x^5-x-1)[1] \\ _Charles R Greathouse IV_, Apr 14 2014

%Y Cf. A001622, A039922 (continued fraction), A060006, A060007.

%K nonn,easy,cons

%O 1,3

%A _Harry J. Smith_, May 03 2009