p25.py

"""
The Fibonacci sequence is defined by the recurrence relation:

Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:

F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
"""
def main():
	# iterative Fibonacci

	fib_last_term = 1
	fib_2nd_last_term = 1
	index = 2
	while len(str(fib_last_term)) != 1000:
		temp = fib_last_term
		fib_last_term+=fib_2nd_last_term
		fib_2nd_last_term = temp
		index+=1

	print("Index of the 1st term in the Fib. seq. to contain 1000 digits:", index, "\nActual value of this Fib. seq. term:", fib_last_term)

if __name__ == "__main__":
	main()