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

Author

Iain Fox, Oct 10 2017

Keywords

• cons
• nonn

Comments

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

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

Examples

			1.570147312196054362910665...
		

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

Crossrefs

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

Programs

Mathematica

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

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));

Extensions

More terms from Andrey Zabolotskiy, Oct 12 2017