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A117605 Decimal expansion of the real solution to equation x^3 + 3*x = 2. 4
5, 9, 6, 0, 7, 1, 6, 3, 7, 9, 8, 3, 3, 2, 1, 5, 2, 3, 1, 1, 2, 8, 0, 5, 4, 1, 4, 3, 9, 9, 6, 8, 1, 8, 2, 8, 1, 1, 3, 3, 2, 5, 4, 9, 4, 3, 9, 6, 2, 1, 3, 1, 9, 4, 3, 2, 4, 7, 9, 0, 8, 3, 0, 3, 6, 0, 0, 5, 1, 6, 2, 6, 8, 6, 2, 0, 8, 9, 1, 8, 5, 8, 7, 1, 6, 6, 0, 3, 3, 7, 5, 4, 2, 8, 4, 7, 5, 4, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A014176 Decimal expansion of the silver mean, 1+sqrt(2). Interestingly, when we look for x=0.596071637983321523112805414399681828113325, the original Inverse Symbolic Calculator replies: "... Roots of polynomials of 4th degree (coeffs: -9..9) 5960716379833215 = 10+15*x+5*x^3" - with wrong sign of the first term.

Let p(n,x) denote the n-th Maclaurin polynomial of e^x, and let p'(n,x) denote its derivative. Then p'(n+1,x) = p(n,x), so that the real zero r of p(n,x), for odd n, is also the value of x that minimizes p(n+1,x). Let y = 0.5960716... . Then for n = 3, we have r = - y - 1; see A332324 for the minimal value of p(4,x). - Clark Kimberling, Feb 13 2020

LINKS

Table of n, a(n) for n=0..99.

Original Inverse Symbolic Calculator

FORMULA

x = (1+sqrt(2))^(1/3) - 1/(1+sqrt(2))^(1/3).

EXAMPLE

x = 0.596071637983321523112805414399681828113325...

MATHEMATICA

RealDigits[N[Solve[3*z+z^3==2, z][[1, 1, 2]], 100]][[1]]

CROSSREFS

Cf. A014176, A332324.

Sequence in context: A133742 A134879 A051158 * A303983 A073003 A087498

Adjacent sequences:  A117602 A117603 A117604 * A117606 A117607 A117608

KEYWORD

cons,nonn

AUTHOR

Zak Seidov, Apr 27 2006

EXTENSIONS

Website URL and name (changed from "Plouffe's Inverter") updated by Jon E. Schoenfield, Feb 28 2020

STATUS

approved

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Last modified April 17 02:26 EDT 2021. Contains 343059 sequences. (Running on oeis4.)