Fibonacci Fantasy

Copyright © 2000 by Paul Niquette. All rights reserved.

Start with the number 0 and the number 1. Add them together. You get 1. Now add that 1 to the previous 1. This time you get 2. Are we going too fast here? Now add the 2 to the immediately preceding 1, for a sum of 3. So far, we have produced the following series of 'natural' numbers: 0, 1, 1, 2, 3. Continuing in like manner, adding the 3 we just computed to the 2 from one step ago, and we get the next number in the series, 5. And so forth, 8, 13, 21,...

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

These numbers form the 'Fibonacci Sequence.' Its discovery dates back to the early thirteenth century and to the most distinguished mathematician of the Middle Ages, Leonardo Fibonacci, also known as Leonardo of Pisa. He invented the first 'recursive number sequence.'

Over the centuries, countless mathematicians have devoted their careers to the study of such integer sequences, discovering esoteric properties in them. Philosophers have joined in the fun, writing recondite monographs to one another about the mystical attributes of Fibonacci numbers.

Today's number theorists and computer scientists continue the arcane tradition. As recently as 1962, a group of enthusiasts founded 'A Fibonacci Association' -- in California, of course.

Fibonacci numbers grow big fast. The 41st entry in the series amounts to more than 100 million. You can prove that for yourself in just a few minutes.

Given that...
86,267,571,272 a Fibonacci number.
What is the next number in sequence?