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A230156 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=8.

%I A230156 #15 Dec 05 2016 10:39:01
%S A230156 9,2,1,5,9,9,3,1,9,6,3,3,9,8,3,0,0,6,2,9,9,4,3,0,3,1,5,2,0,1,9,6,9,3,
%T A230156 9,4,2,5,3,6,8,0,3,8,4,2,5,3,3,7,0,7,8,9,8,7,9,6,5,4,5,1,6,4,4,4,7,1,
%U A230156 4,5,9,4,2,4,9,1,7,4,3,0,8,2,7,9,1,7,9
%N A230156 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=8.
%C A230156 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-8.
%H A230156 Paolo P. Lava, <a href="/A230156/b230156.txt">Table of n, a(n) for n = 0..1000</a>
%e A230156 0.9215993196339830062994303152019693942536803842533707898...
%p A230156 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230156 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230156 print(evalf(a,1000)); end: P(1000,-8);
%t A230156 Root[x^9 + x^8 - 1, 1] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y A230156 Cf. A075778, A230151-A230155, A230157, A230158.
%K A230156 nonn,cons
%O A230156 0,1
%A A230156 _Paolo P. Lava_, Oct 11 2013