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

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, 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, 8, 6, 0, 9, 3, 3, 0, 8, 7, 1, 3, 7, 0, 3, 1, 9, 6, 2

Offset: 0

Author

Paolo P. Lava, Oct 11 2013

Keywords

• nonn
• cons

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-3.

Examples

			0.8191725133961644396995711883424270403484978325537129656...
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 0..1000 (corrected by _Sean A. Irvine_)
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A086106 (other real root).

Cf. A075778, A230152-A230158.

Programs

Maple

with(numtheory); P:=proc(q,h) local a,n; a:=(q+1)^(1/h);
for n from q by -1 to 1 do a:=(1+a)^(1/h);od;
print(evalf(a,1000)); end: P(1000,-3);

Mathematica

Root[(#^4+#^3-1)&, 2] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

PARI

polrootsreal(x^4+x^3-1)[2] \\ Charles R Greathouse IV, Feb 04 2025