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A230162 Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=9.

%I A230162 #12 Jul 31 2017 10:43:42
%S A230162 1,0,8,5,0,7,0,2,4,5,4,9,1,4,5,0,8,2,8,3,3,6,8,9,5,8,6,4,0,9,7,3,1,4,
%T A230162 2,3,4,0,5,0,6,5,3,6,3,1,0,3,0,8,9,6,5,8,1,4,6,8,6,1,5,5,3,3,3,6,5,1,
%U A230162 8,0,4,9,9,4,0,1,1,5,7,1,9,9,7,4,1,9,3
%N A230162 Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=9.
%C A230162 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=9.
%H A230162 Paolo P. Lava, <a href="/A230162/b230162.txt">Table of n, a(n) for n = 1..1000</a>
%e A230162 1.0850702454914508283368958640973142340506536310308965814...
%p A230162 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230162 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230162 print(evalf(a,1000)); end: P(1000,9);
%t A230162 Root[(#^9-#-1)&, 1] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%t A230162 RealDigits[x/.FindRoot[x^9-x-1==0,{x,1},WorkingPrecision->100]][[1]] (* _Harvey P. Dale_, Jul 31 2017 *)
%Y A230162 Cf. A001622, A060006, A060007, A160155, A230159-A230161, A230163.
%K A230162 nonn,cons
%O A230162 1,3
%A A230162 _Paolo P. Lava_, Oct 11 2013