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A230155 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=7.

%I A230155 #15 Dec 05 2016 10:41:03
%S A230155 9,1,1,5,9,2,3,5,3,4,8,2,0,5,4,9,1,8,6,2,8,6,7,3,6,7,2,4,9,4,0,5,0,1,
%T A230155 7,7,3,7,5,8,8,4,6,9,4,3,6,1,4,1,3,9,4,6,9,5,5,7,6,2,6,5,3,9,2,3,4,4,
%U A230155 3,4,8,8,2,5,2,4,0,4,1,2,8,9,8,9,5,8,0,1,2,7,5,4,7,3,9,0,7,0,9,4,3,0,0,0,1,9,6,8,6,8,7,3,6,8,9,5,6,5,8,7,3,2,9,6,8,1,6,2,9,4
%N A230155 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=7.
%C A230155 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-7.
%H A230155 Paolo P. Lava, <a href="/A230155/b230155.txt">Table of n, a(n) for n = 0..1000</a>
%e A230155 0.9115923534820549186286736724940501773758846943614139469...
%p A230155 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230155 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230155 print(evalf(a,1000)); end: P(1000,-7);
%t A230155 Root[x^8 + x^7 - 1, 2] // RealDigits[#, 10, 130]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y A230155 Cf. A075778, A230151-A230154, A230156-A230158.
%K A230155 nonn,cons
%O A230155 0,1
%A A230155 _Paolo P. Lava_, Oct 11 2013