Iterating through the Fibonacci sequence

Question

so i'd like to iterate through the Fibonacci sequence (but this could apply to any non-arithmetic sequence). i've written a function fibonacci:

from math import sqrt
def F(n):
    return ((1+sqrt(5))**n-(1-sqrt(5))**n)/(2**n*sqrt(5))

which returns the fibonacci number for any given input. this bit seems to work OK. However, I'd like to include a couple of conditions, like even numbers and F(n) below a certain limit. I tried using an if loop like this:

def ser():
    count = 0
    for i in F(n):
        if F(n) <= 4000000 and F(n) % 2 == 0:
            count = count + F(n)

But it seems like you can't use F(n) in the iteration for loop like I did. I'm a complete novice at python, so how would be best to use the F(n) function I created to iterate over the sequence? Thanks

Answer 1

What is the range of n that you are looking to run the fibonacci number on?
Your definition of fibonacci is in a closed form, so you need to give each number you want to calculate:

import itertools
count = 0
for n in itertools.count(1):
    if F(n) > 4000000:
        break
    if F(n) % 2 == 0:
        count += F(n)

You can use a generator form of fibonacci and use itertools.takewhile() to limit the output:

def F():
    a,b = 0,1
    yield b
    while True:
        a, b = b, a + b
        yield b

count = sum(f for f in it.takewhile(lambda x: x <= 4000000, F()) if f % 2 == 0)