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A230159 Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=6.

%I A230159 #17 Mar 03 2023 22:33:26
%S A230159 1,1,3,4,7,2,4,1,3,8,4,0,1,5,1,9,4,9,2,6,0,5,4,4,6,0,5,4,5,0,6,4,7,2,
%T A230159 8,4,0,2,7,9,6,6,7,2,2,6,3,8,2,8,0,1,4,8,5,9,2,5,1,4,9,5,5,1,6,6,8,2,
%U A230159 3,6,8,9,3,9,9,9,8,4,2,6,7,1,2,7,9,6,8
%N A230159 Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=6.
%C A230159 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=6.
%H A230159 Paolo P. Lava, <a href="/A230159/b230159.txt">Table of n, a(n) for n = 1..1000</a> (corrected by _Sean A. Irvine_)
%e A230159 1.1347241384015194926054460545064728402796672263828014859...
%p A230159 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230159 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230159 print(evalf(a,1000)); end: P(1000,6);
%t A230159 Root[x^6 - x - 1, 2] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%Y A230159 Cf. A001622, A060006, A060007, A160155, A230160-A230163.
%K A230159 nonn,cons
%O A230159 1,3
%A A230159 _Paolo P. Lava_, Oct 11 2013