One of the more interesting things about the Fibonacci sequence is the interplay between the numbers; how they interrelate and their "behaviors." Some of the interactions are simple fun tricks, such as those in the children's book where I originally discovered the sequence to more complex paradoxes.
A few examples:
| 1 | 5 | 89 |
| 1 | 8 | 144 |
| 2 | 13 | 233 |
| 3 | 21 | 377 |
| 5 | 34 | 610 |
| 8 | 55 | 987 |
| 13 | 89 | 1,597 |
| 21 | 144 | 2,584 |
| 34 | 233 | 4,1841 |
| +55 | +377 | +6,765 |
| _____ | _____ | _______ |
| 143 / 11=13 | 979 / 11=89 | 17,567 / 11=1,579 |
Every 3rd Fibonacci number is divisible by 2.
Every 4th Fibonacci number is divisible by 3.
Every 5th Fibonacci number is divisible by 5.
Every 6th Fibonacci number is divisible by 8.
Every 7th Fibonacci number is divisible by 13.
Every 8th Fibonacci number is divisible by 21.
| Fibonacci Number | Prime Factors | Fibonacci Number | Prime Factors |
|---|---|---|---|
| 1 | 1 | 55 | 5x11 |
| 1 | 1 | 89 | 89 |
| 2 | 2 | 144* | 2x2x2x2x3x3* |
| 3 | 3 | 233 | 233 |
| 5 | 5 | 377 | 13x29 |
| 8 | 2x2x2 | 610 | 2x5x61 |
| 13 | 13 | 987 | 3x7x47 |
| 21 | 3x7 | 1597 | 1579 |
| 34 | 2x17 | 2584 | 2x2x2x17x19 |
* The 12th Fibonacci number (144) is the square of 12.
It is also the only square number in the entire sequence
well, as long as you don't count the number 1.
Here is a great site with some interesting Fibonacci Puzzles
Natural Fibonacci (Previous Page)
Fibonacci Goes Gold (Next)
Aestetically Pleasing Fibonacci?