A230152 Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=4.

8, 5, 6, 6, 7, 4, 8, 8, 3, 8, 5, 4, 5, 0, 2, 8, 7, 4, 8, 5, 2, 3, 2, 4, 8, 1, 5, 3, 1, 2, 4, 3, 4, 3, 6, 9, 8, 3, 1, 3, 9, 9, 9, 4, 5, 4, 9, 3, 7, 5, 2, 6, 2, 5, 5, 7, 6, 4, 1, 2, 8, 1, 0, 3, 4, 6, 7, 9, 8, 4, 2, 4, 6, 2, 2, 9, 0, 4, 3, 6, 2, 1, 1, 0, 3, 5, 1

Offset

0,1

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=-4.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000 (corrected by Sean A. Irvine)

Index entries for algebraic numbers, degree 5

Example

0.8566748838545028748523248153124343698313999454937526255...

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, -4);

Mathematica

Root[x^5 + x^4 - 1, 1] // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Feb 18 2014 *)

Crossrefs

Cf. A075778, A230151, A230153-A230158, A377080.

Sequence in context: A199059 A065415 A154013 * A099002 A365281 A021898

Adjacent sequences: A230149 A230150 A230151 * A230153 A230154 A230155

Keyword

nonn,cons

Author

Paolo P. Lava, Oct 11 2013

Status

approved