A160155 Decimal expansion of the one real root of x^5-x-1.

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, 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, 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

Offset

1,3

Comments

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

David W. Boys, The maximal modulus of an algebraic integer, Math. Comp. 45 (1985) 243-249, table page S18.

Qiang Wu, The smallest Perron numbers, Math. Comp. 79 (2010) 2387-2394

Index entries for algebraic numbers, degree 5

Formula

Equals (1 + (1 + (1 + (1 + (1 + ...)^(1/5))^(1/5))^(1/5))^(1/5))^(1/5). - Ilya Gutkovskiy, Dec 15 2017

Example

1.16730397826141868425604589985484218072056037152548903914008244927565...

Mathematica

RealDigits[Root[x^5-x-1, x, 1], 10, 105] // First (* Jean-François Alcover, Jul 09 2015 *)

Prog

(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));
(PARI) polrootsreal(x^5-x-1)[1] \\ Charles R Greathouse IV, Apr 14 2014

Crossrefs

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

Sequence in context: A267251 A259526 A108664 * A277135 A153628 A154972

Adjacent sequences: A160152 A160153 A160154 * A160156 A160157 A160158

Keyword

nonn,easy,cons

Author

Harry J. Smith, May 03 2009

Status

approved