Definitions: the Fibonacci numbers can be rather simply defined by the following:

1. StartMore formally: [F^{1}with the numbers 1 and 2.2. Add them together to make the next number (3).

3. Then form the next number in sequence by adding the previous two together.

The resulting sequence begins like this:

F_{1}to F_{19}:

1,, 8,2, 3, 5, 21, 34, 55,13, 144,89, 377, 610, 987,233, 2584, 4181, 6765...1597

The numbers seem to pop up in perhaps unexpected places (e.g., cornfields, seashells, Greek monuments).

A variety of unsolved problems concerning the numbers remain (e.g., "are there infinitely many prime Fibonacci's?", "what happens when the start numbers are varied?", "what sorts of sequences arise modulo n?").

^{1} It is interesting to note that while most
modern presentations begin the sequence (1,1,2,3,...), Fibonacci himself
omitted the initial 1 and began, instead, with F_{2}=2.