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

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

Offset

1,3

Comments

Also decimal expansion of (1+(1+(1+ ... )^(1/k))^(1/k))^(1/k), with k integer and k<0. Case k=10.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Index entries for algebraic numbers, degree 10.

Example

1.0757660660868371580595995241652758206925302476392032794...

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, 10);

Mathematica

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

Prog

(PARI) polrootsreal(x^10-x-1)[2] \\ Charles R Greathouse IV, Feb 11 2025

Crossrefs

Cf. A001622, A060006, A060007, A160155, A230159-A230162.

Sequence in context: A021136 A214444 A194657 * A143297 A195348 A072449

Adjacent sequences: A230160 A230161 A230162 * A230164 A230165 A230166

Keyword

nonn,cons

Author

Paolo P. Lava, Oct 11 2013

Status

approved