A337571 Decimal expansion of the real positive solution to x^4 = x+4.

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

Offset: 1

Author

Michal Paulovic, Sep 01 2020

Keywords

• nonn
• cons

Comments

x = (4 + (4 + (4 + ... )^(1/4))^(1/4))^(1/4).

The negative value (-1.5337511687...) is the real negative solution to x^4 = 4-x.

Examples

			1.5337511687552...
		

Links

• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A337570, A060007, A294644.

Programs

MATLAB

format long; solve('x^4-x-4=0'); ans(1), (eval(ans))

Mathematica

RealDigits[x /. FindRoot[x^4 - x - 4, {x, 1}, WorkingPrecision -> 100], 10, 90][[1]] (* Amiram Eldar, Sep 03 2020 *)

PARI

solve(n=0,2,n^4-n-4)

PARI

polroots(n^4-n-4)[2]

PARI

polrootsreal(n^4-n-4)[2] \\ Charles R Greathouse IV, Oct 27 2023

Formula

Equals sqrt(sqrt(1/s) - s/16) + sqrt(s/16) where s = (sqrt(16804864/27) + 32)^(1/3) - (sqrt(16804864/27) - 32)^(1/3). [Simplified by Michal Paulovic, Jun 22 2021]