cp's OEIS Frontend

A230151 Decimal expansion of the positive real solution of the equation x^4 + x^3 - 1 = 0.

%I A230151 #27 Feb 04 2025 10:30:44
%S A230151 8,1,9,1,7,2,5,1,3,3,9,6,1,6,4,4,3,9,6,9,9,5,7,1,1,8,8,3,4,2,4,2,7,0,
%T A230151 4,0,3,4,8,4,9,7,8,3,2,5,5,3,7,1,2,9,6,5,6,6,7,6,8,0,2,5,3,1,6,7,4,2,
%U A230151 8,6,0,9,3,3,0,8,7,1,3,7,0,3,1,9,6,2
%N A230151 Decimal expansion of the positive real solution of the equation x^4 + x^3 - 1 = 0.
%C A230151 Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-3.
%H A230151 Paolo P. Lava, <a href="/A230151/b230151.txt">Table of n, a(n) for n = 0..1000</a> (corrected by _Sean A. Irvine_)
%H A230151 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%e A230151 0.8191725133961644396995711883424270403484978325537129656...
%p A230151 with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
%p A230151 for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
%p A230151 print(evalf(a,1000)); end: P(1000,-3);
%t A230151 Root[(#^4+#^3-1)&, 2] // RealDigits[#, 10, 100]& // First (* _Jean-François Alcover_, Feb 18 2014 *)
%o A230151 (PARI) polrootsreal(x^4+x^3-1)[2] \\ _Charles R Greathouse IV_, Feb 04 2025
%Y A230151 Cf. A086106 (other real root).
%Y A230151 Cf. A075778, A230152-A230158.
%K A230151 nonn,cons
%O A230151 0,1
%A A230151 _Paolo P. Lava_, Oct 11 2013