A293506 Decimal expansion of real root of x^5 - x^4 - x^2 - 1.

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

Offset

1,2

Comments

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

The ratio of successive terms of A122115 converges to this number.

Links

Iain Fox, Table of n, a(n) for n = 1..20000

Hans Walser, Funktionenfolge [in German]

Eric Weisstein's World of Mathematics, Pisot Number

Wikipedia, Pisot-Vijayaraghavan number

Index entries for algebraic numbers, degree 5

Example

1.570147312196054362910665...

Mathematica

First@ RealDigits[Root[#^5 - #^4 - #^2 - 1 &, 1], 10, 87] (* Michael De Vlieger, Oct 23 2017 *)

Prog

(PARI) solve(x=1, 2, x^5 - x^4 - x^2 - 1) \\ Michel Marcus, Oct 11 2017
(PARI)  default(realprecision, 20080); x=solve(x=1, 2, x^5 - x^4 - x^2 - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b293506.txt", n, " ", d));

Crossrefs

Cf. A060006, A086106, A228777, A092526, A293508, A293509, A293557, A122115, A293560 (inverse).

Sequence in context: A134756 A178902 A176713 * A011350 A295823 A161018

Adjacent sequences: A293503 A293504 A293505 * A293507 A293508 A293509

Keyword

cons,nonn

Author

Iain Fox, Oct 10 2017

Extensions

More terms from Andrey Zabolotskiy, Oct 12 2017

Status

approved