A293509 Decimal expansion of real root of x^5 - x^3 - x^2 - x - 1.

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, 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, 6, 3, 0, 2, 3, 2, 1, 4, 0, 8, 2, 2, 8, 1, 4, 3, 6, 7, 8

Offset: 1

Author

Iain Fox, Oct 11 2017

Keywords

• cons
• nonn

Comments

This root is also the sixth smallest of the Pisot numbers.

Examples

			1.53415774491426691543597007610937570188254503851659513536853186300806302321...
		

Links

• Iain Fox, Table of n, a(n) for n = 1..20000
• Eric Weisstein's World of Mathematics, Pisot Number.
• Wikipedia, Pisot-Vijayaraghavan number
• Index entries for algebraic numbers, degree 5

Crossrefs

Cf. A060006, A086106, A228777, A092526, A293506, A293508, A293557.

Programs

Mathematica

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 *)

PARI

solve(x=1, 2, x^5 - x^3 - x^2 - x - 1) \\ Michel Marcus, Oct 13 2017

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

PARI

polrootsreal(x^5 - x^3 - x^2 - x - 1)[1] \\ Charles R Greathouse IV, Nov 04 2017