Python Challenges: Find the index of the first term in the Fibonacci sequence to contain 500 digits
Python Challenges - 1: Exercise-49 with Solution
Write a Python program to find the index of the first term in the Fibonacci sequence to contain 500 digits.
In mathematics, the Fibonacci numbers, commonly denoted Fn form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1
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.
Sample Solution:
Python Code:
import itertools
def Fibonacci_sequence(n):
DIGITS = n
prev_num = 1
cur_num = 0
for i in itertools.count():
# At this point, prev = fibonacci(i - 1) and cur = fibonacci(i)
if len(str(cur_num)) > DIGITS:
raise RuntimeError("Not found")
elif len(str(cur_num)) == DIGITS:
return str(i)
prev_num, cur_num = cur_num, prev_num + cur_num
print(Fibonacci_sequence(500))
Sample Output:
2390
Flowchart:
Python Code Editor:
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Previous: Write a Python program to find the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Next: Write a Python program that takes a string and encode it that the amount of symbols would be represented by integer and the symbol.
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Python: Tips of the Day
Find current directory and file's directory:
To get the full path to the directory a Python file is contained in, write this in that file:
import os dir_path = os.path.dirname(os.path.realpath(__file__))
(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)
To get the current working directory use
import os cwd = os.getcwd()
Documentation references for the modules, constants and functions used above:
- The os and os.path modules.
- The __file__ constant
- os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
- os.path.dirname(path) (returns "the directory name of pathname path")
- os.getcwd() (returns "a string representing the current working directory")
- os.chdir(path) ("change the current working directory to path")
Ref: https://bit.ly/3fy0R6m
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