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#!/usr/bin/env python3
# Challenge 155
#
# TASK #2 > Pisano Period
# Submitted by: Mohammad S Anwar
# Write a script to find the period of the 3rd Pisano Period.
#
# In number theory, the nth Pisano period, written as p(n), is the period with
# which the sequence of Fibonacci numbers taken modulo n repeats.
#
# The Fibonacci numbers are the numbers in the integer sequence:
#
# 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, ...
# For any integer n, the sequence of Fibonacci numbers F(i) taken modulo n is
# periodic. The Pisano period, denoted p(n), is the value of the period of this
# sequence. For example, the sequence of Fibonacci numbers modulo 3 begins:
#
# 0, 1, 1, 2, 0, 2, 2, 1,
# 0, 1, 1, 2, 0, 2, 2, 1,
# 0, 1, 1, 2, 0, 2, 2, 1, ...
# This sequence has period 8, so p(3) = 8.
from math import isqrt
order = 3
def fibonacci_series(n):
fibs = [0, 1]
for i in range(2, n):
fibs.append(fibs[-1] + fibs[-2])
return fibs
def is_period(period, n):
base = n[0:period]
ord1 = n[period:2*period]
ord2 = n[2*period:3*period]
if base != ord1:
return 0
if base != ord2:
return 0
return 1
def find_period(n):
period = 1
while True:
if 3 * period > len(n):
return 0
if is_period(period, n):
return period
period += 1
return 0
fibs = fibonacci_series(100)
fibs_mod = [fib % order for fib in fibs]
print(find_period(fibs_mod))
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