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A230153 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=5.

%I A230153 #16 Dec 05 2016 10:40:59
%S A230153 8,8,1,2,7,1,4,6,1,6,3,3,5,6,9,5,9,4,4,0,7,6,4,9,1,6,2,8,4,1,3,7,2,0,
%T A230153 2,5,2,7,9,1,9,3,9,7,9,3,7,8,8,9,5,2,6,3,6,0,6,7,6,3,8,4,6,9,5,7,7,6,
%U A230153 8,7,6,8,4,6,8,6,3,2,4,6,7,3,5,5,9,1,0
%N A230153 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=5.
%C A230153 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-5.
%H A230153 Paolo P. Lava, <a href="/A230153/b230153.txt">Table of n, a(n) for n = 0..1000</a>
%e A230153 0.8812714616335695944076491628413720252791939793788952636...
%p A230153 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230153 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230153 print(evalf(a,1000)); end: P(1000,-5);
%t A230153 Root[x^6 + x^5 - 1, 2] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y A230153 Cf. A075778, A230151, A230152, A230154-A230158.
%K A230153 nonn,cons
%O A230153 0,1
%A A230153 _Paolo P. Lava_, Oct 11 2013