project_euler.problem_025.sol1

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?

Functions

fibonacci(→ int)	Computes the Fibonacci number for input n by iterating through n numbers
fibonacci_digits_index(→ int)	Computes incrementing Fibonacci numbers starting from 3 until the length
solution(→ int)	Returns the index of the first term in the Fibonacci sequence to contain

Module Contents

project_euler.problem_025.sol1.fibonacci(n: int) → int

Computes the Fibonacci number for input n by iterating through n numbers and creating an array of ints using the Fibonacci formula. Returns the nth element of the array.

>>> fibonacci(2)
1
>>> fibonacci(3)
2
>>> fibonacci(5)
5
>>> fibonacci(10)
55
>>> fibonacci(12)
144

project_euler.problem_025.sol1.fibonacci_digits_index(n: int) → int

Computes incrementing Fibonacci numbers starting from 3 until the length of the resulting Fibonacci result is the input value n. Returns the term of the Fibonacci sequence where this occurs.

>>> fibonacci_digits_index(1000)
4782
>>> fibonacci_digits_index(100)
476
>>> fibonacci_digits_index(50)
237
>>> fibonacci_digits_index(3)
12

project_euler.problem_025.sol1.solution(n: int = 1000) → int

Returns the index of the first term in the Fibonacci sequence to contain n digits.

>>> solution(1000)
4782
>>> solution(100)
476
>>> solution(50)
237
>>> solution(3)
12