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A114431 Decimal expansion of the real solution of x^3-x^2-2x-4=0. 1
2, 4, 6, 7, 5, 0, 3, 8, 5, 7, 0, 5, 6, 5, 1, 7, 5, 7, 6, 3, 8, 1, 8, 8, 6, 7, 5, 5, 3, 5, 8, 7, 8, 6, 0, 7, 0, 3, 8, 2, 2, 5, 4, 4, 7, 5, 0, 6, 2, 3, 7, 2, 9, 8, 8, 4, 6, 4, 0, 1, 9, 7, 7, 4, 0, 5, 5, 0, 7, 5, 1, 9, 3, 5, 9, 1, 7, 7, 3, 3, 9, 7, 1, 5, 8, 1, 5, 9, 5, 1, 6, 3, 4, 9, 2, 3, 8, 6, 3, 5, 7, 5, 3, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The solution of the equation is twice the value of an upper bound on randomly generated Fibonacci-like sequences.

LINKS

Table of n, a(n) for n=0..104.

Eran Makover and Jeffrey McGowan, An elementary proof that random Fibonacci sequences grow exponentially, Journal of Number Theory, Volume 121, Issue 1, November 2006, Pages 40-44. (arXiv:math/0510159 [math.NT])

MATHEMATICA

RealDigits[x/.FindRoot[x^3-x^2-2x==4, {x, 2}, WorkingPrecision-> 120], 10, 120] [[1]] (* or *) RealDigits[(1+Surd[64-3*Sqrt[417], 3]+ Surd[ 64+ 3* Sqrt[ 417], 3])/3, 10, 120][[1]] (* Harvey P. Dale, Dec 02 2017 *)

PROG

(PARI) default(realprecision, 105); 1/3*(1+(64-3*sqrt(417))^(1/3)+(64+3*sqrt(417))^(1/3)) \\ Michel Marcus, Jun 14 2013

CROSSREFS

Cf. A114427.

Sequence in context: A091476 A257578 A272665 * A167689 A058184 A087777

Adjacent sequences:  A114428 A114429 A114430 * A114432 A114433 A114434

KEYWORD

cons,nonn

AUTHOR

Stefan Steinerberger, Feb 13 2006

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)