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A230152 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=4.

%I A230152 #24 Oct 15 2024 11:51:58
%S A230152 8,5,6,6,7,4,8,8,3,8,5,4,5,0,2,8,7,4,8,5,2,3,2,4,8,1,5,3,1,2,4,3,4,3,
%T A230152 6,9,8,3,1,3,9,9,9,4,5,4,9,3,7,5,2,6,2,5,5,7,6,4,1,2,8,1,0,3,4,6,7,9,
%U A230152 8,4,2,4,6,2,2,9,0,4,3,6,2,1,1,0,3,5,1
%N A230152 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=4.
%C A230152 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-4.
%H A230152 Paolo P. Lava, <a href="/A230152/b230152.txt">Table of n, a(n) for n = 0..1000</a> (corrected by _Sean A. Irvine_)
%H A230152 <a href="/index/Al#algebraic_05">Index entries for algebraic numbers, degree 5</a>
%e A230152 0.8566748838545028748523248153124343698313999454937526255...
%p A230152 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230152 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230152 print(evalf(a,1000)); end: P(1000,-4);
%t A230152 Root[x^5 + x^4 - 1, 1] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y A230152 Cf. A075778, A230151, A230153-A230158, A377080.
%K A230152 nonn,cons
%O A230152 0,1
%A A230152 _Paolo P. Lava_, Oct 11 2013