Fibonacci Sequence

Here is the Fibonacci sequence made in Lego in the same way.

Just as in the number line you can see how the colours repeat in a regular pattern. In the Fibonacci sequence the blue block repeats every third time, and the red block every fourth time, and so on.

So we can see that
$2 | F_3, F_6, F_9, \ldots$
$3 | F_4, F_8, F_{12}, \ldots$
$5 | F_5, F_{10}, F_{15}, \ldots$

Or another way to write it is

$F_3 | F_3, F_6, F_9, \ldots$

$F_4 | F_4, F_8, F_{12}, \ldots$

$F_5 | F_5, F_{10}, F_{15}, \ldots$

So the 'F' numbers make a number line just like the counting numbers, except that F₂ is not 'prime' ... this means that F₄ has to be an 'F-prime'.