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A337571 Decimal expansion of the real positive solution to x^4 = x+4. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..97.

FORMULA

Equals sqrt(W / 12 - 4 / W) + sqrt(4 / W - W / 12 + 1 / sqrt(4 * W / 3 - 64 / W)) where W = (27/2 + sqrt(443097/4))^(1/3).

EXAMPLE

1.5337511687552...

MATHEMATICA

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

PROG

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

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

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

CROSSREFS

Cf. A337570, A060007, A294644.

Sequence in context: A019624 A120275 A021656 * A244683 A263157 A084538

Adjacent sequences:  A337568 A337569 A337570 * A337572 A337573 A337574

KEYWORD

nonn,cons

AUTHOR

Michal Paulovic, Sep 01 2020

STATUS

approved

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Last modified January 21 02:20 EST 2021. Contains 340332 sequences. (Running on oeis4.)