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A230158 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=10.

%I A230158 #16 Feb 07 2025 13:18:42
%S A230158 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 A230158 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 A230158 9,5,0,6,3,9,2,7,3,5,4,3,2,6,4,9,6,9,7
%N A230158 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=10.
%C A230158 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-10.
%H A230158 Paolo P. Lava, <a href="/A230158/b230158.txt">Table of n, a(n) for n = 0..1000</a>
%H A230158 <a href="/index/Al#algebraic_10">Index entries for algebraic numbers, degree 10</a>.
%e A230158 0.9360691110777583783971914875702962034360714782064850849...
%p A230158 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230158 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230158 print(evalf(a,1000)); end: P(1000,-10);
%t A230158 Root[x^11 + x^10 - 1, 1] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%o A230158 (PARI) polrootsreal(x^11+x^10-1)[1] \\ _Charles R Greathouse IV_, Feb 07 2025
%Y A230158 Cf. A075778, A230151-A230157.
%K A230158 nonn,cons
%O A230158 0,1
%A A230158 _Paolo P. Lava_, Oct 11 2013