%I #16 Dec 05 2016 10:40:28

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

%T 2,5,4,3,5,3,2,5,8,5,3,0,0,2,0,2,4,8,3,3,6,3,0,2,0,5,5,4,5,2,1,5,0,9,

%U 8,7,8,5,3,0,6,5,4,2,7,2,6,2,1,3,5,0,7

%N Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=9.

%C Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-9.

%H Paolo P. Lava, <a href="/A230157/b230157.txt">Table of n, a(n) for n = 0..1000</a>

%e 0.9295701282320228642044130369144641254353258530020248336...

%p with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);

%p for n from q by -1 to 1 do a:=(1+a)^(1/h);od;

%p print(evalf(a,1000)); end: P(1000,-9);

%t Root[x^10 + x^9 - 1, 2] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)

%Y Cf. A075778, A230151-A230156, A230158.

%K nonn,cons

%O 0,1

%A _Paolo P. Lava_, Oct 11 2013