A114427 Decimal expansion of the real solution of x^3-x^2-x-4=0.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..105.

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])

Example

The solution of the equation is 2.2418965630344798557894...

Mathematica

RealDigits[1/3 (1+(1/2 (119-3 Sqrt[1545]))^(1/3)+(1/2 (119+3 Sqrt[ 1545]))^(1/3)), 10, 120][[1]] (* Harvey P. Dale, Jun 09 2011 *)

Crossrefs

Cf. A114431.

Sequence in context: A152593 A243548 A105478 * A129355 A080963 A133692

Adjacent sequences: A114424 A114425 A114426 * A114428 A114429 A114430

Keyword

cons,nonn

Author

Stefan Steinerberger, Feb 13 2006

Status

approved