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A160155 Decimal expansion of the one real root of x^5-x-1. 14
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 (list; constant; graph; refs; listen; history; text; internal format)
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
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
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
KEYWORD
nonn,easy,cons
AUTHOR
Harry J. Smith, May 03 2009
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)