A243629 Fibonacci's solution to x^3 + 2x^2 + 10x = 20.

1, 22, 7, 42, 33, 4, 40

Offset

0,2

Comments

Fibonacci attempted to solve x^3 + 2x^2 + 10x = 20 and managed to approximate an answer in base 60 with this sequence without a calculator or computer, but he gave a(6) as 40 instead of the correct answer of 38 (see A159990). Unfortunately, Fibonacci did not explain how he calculated this sequence, so it is not possible to explore the precision to a greater degree.

References

Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers. New York: Prometheus Books (2007): 21.

Links

Table of n, a(n) for n=0..6.

Example

x = 1 + 22/60 + 7/60^2 + 42/60^3 + 33/60^4 + 4/60^5 + 40/60^6. Then x^3 + 2x^2 + 10x = 20.0000000006719323...

Crossrefs

Cf. A159990 shows the sequence corrected.

Sequence in context: A194708 A069285 A159990 * A040466 A133682 A134911

Adjacent sequences: A243626 A243627 A243628 * A243630 A243631 A243632

Keyword

nonn

Author

Jason Chabora, Jun 10 2014

Status

approved