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A230163 Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=10.

%I A230163 #15 Feb 11 2025 14:15:56
%S A230163 1,0,7,5,7,6,6,0,6,6,0,8,6,8,3,7,1,5,8,0,5,9,5,9,9,5,2,4,1,6,5,2,7,5,
%T A230163 8,2,0,6,9,2,5,3,0,2,4,7,6,3,9,2,0,3,2,7,9,4,7,7,0,6,8,3,9,4,5,4,4,4,
%U A230163 7,2,6,2,6,9,5,8,5,8,2,1,6,1,9,3,3,6,1
%N A230163 Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=10.
%C A230163 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=10.
%H A230163 Paolo P. Lava, <a href="/A230163/b230163.txt">Table of n, a(n) for n = 1..1000</a>
%H A230163 <a href="/index/Al#algebraic_10">Index entries for algebraic numbers, degree 10</a>.
%e A230163 1.0757660660868371580595995241652758206925302476392032794...
%p A230163 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230163 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230163 print(evalf(a,1000)); end: P(1000,10);
%t A230163 Root[x^10 - x - 1, 2] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%o A230163 (PARI) polrootsreal(x^10-x-1)[2] \\ _Charles R Greathouse IV_, Feb 11 2025
%Y A230163 Cf. A001622, A060006, A060007, A160155, A230159-A230162.
%K A230163 nonn,cons
%O A230163 1,3
%A A230163 _Paolo P. Lava_, Oct 11 2013