A293508 Decimal expansion of the positive real root of x^6 - x^5 - x^4 + x^2 - 1.

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

Offset: 1

Author

Iain Fox, Oct 11 2017

Keywords

• cons
• nonn

Comments

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

Examples

			1.501594803539087366377783...
		

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 6.

Crossrefs

Cf. A060006, A086106, A228777, A092526, A293506, A293509, A293557.

Programs

Mathematica

First@ RealDigits[Root[#^6 - #^5 - #^4 + #^2 - 1 &, 2], 10, 105] (* Michael De Vlieger, Oct 23 2017 *)

PARI

solve(x=1, 2, x^6 - x^5 - x^4 + x^2 - 1) \\ Michel Marcus, Oct 11 2017

PARI

{ default(realprecision, 20080); x=solve(x=1, 2, x^6 - x^5 - x^4 + x^2 - 1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b293508.txt", n, " ", d)); }