Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:
1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …
Mathematically, we write it as:
F(n) = F(n) + F(n-1)
This can easily be done in Python, using generators.
def Fibonacci(n):
a, b = 1, 1
while b < n:
yield b
a, b = b, a + bTo print all the Fibonacci numbers less than 4000000,
for i in Fibonacci(4000000):
print i,Output:
>>> 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040 1346269 2178309 3524578
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Actually, that should be:
a, b = 1, 0
Otherwise it won’t emit the first two, 0 and 1.
If you read carefully, I have stated “By starting with 1 and 2, the first 10 terms will be: …”.