A230158 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=10.

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

Offset: 0

Author

Paolo P. Lava, Oct 11 2013

Keywords

• nonn
• cons

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-10.

Examples

			0.9360691110777583783971914875702962034360714782064850849...
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..1000
• Index entries for algebraic numbers, degree 10.

Crossrefs

Cf. A075778, A230151-A230157.

Programs

Maple

with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-10);

Mathematica

Root[x^11 + x^10 - 1, 1] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

PARI

polrootsreal(x^11+x^10-1)[1] \\ Charles R Greathouse IV, Feb 07 2025