How to write the Fibonacci Sequence?

Question

I had originally coded the program wrongly. Instead of returning the Fibonacci numbers between a range (ie. startNumber 1, endNumber 20 should = only those numbers between 1

Answer 1

Fibonacci sequence is: 1, 1, 2, 3, 5, 8, ....

That is f(1) = 1, f(2) = 1, f(3) = 2, ..., f(n) = f(n-1) + f(n-2).

My favorite implementation (simplest and yet achieves a light speed in compare to other implementations) is this:

def fibonacci(n):
    a, b = 0, 1
    for _ in range(1, n):
        a, b = b, a + b
    return b

Test

>>> [fibonacci(i) for i in range(1, 10)]
[1, 1, 2, 3, 5, 8, 13, 21, 34]

Timing

>>> %%time
>>> fibonacci(100**3)
CPU times: user 9.65 s, sys: 9.44 ms, total: 9.66 s
Wall time: 9.66 s

Edit: an example visualization for this implementations.