%I #14 Dec 05 2016 10:39:58

%S 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,

%T 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,

%U 9,5,0,6,3,9,2,7,3,5,4,3,2,6,4,9,6,9,7

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

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

%H Paolo P. Lava, <a href="/A230158/b230158.txt">Table of n, a(n) for n = 0..1000</a>

%e 0.9360691110777583783971914875702962034360714782064850849...

%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,-10);

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

%Y Cf. A075778, A230151-A230157.

%K nonn,cons

%O 0,1

%A _Paolo P. Lava_, Oct 11 2013