Add Python solution to challenge 155

7 files changed, 94 insertions, 5 deletions

diff --git a/challenge-065/paulo-custodio/python/ch-2.py b/challenge-065/paulo-custodio/python/ch-2.py
index 702ed4d413..7d037bdc0d 100644
--- a/challenge-065/paulo-custodio/python/ch-2.py
+++ b/challenge-065/paulo-custodio/python/ch-2.py
@@ -1,4 +1,4 @@
-#!/usr/bin/env perl
+#!/usr/bin/env python3
 
 # Challenge 065
 #
diff --git a/challenge-154/paulo-custodio/python/ch-1.py b/challenge-154/paulo-custodio/python/ch-1.py
index 7deb2cd296..1b121593e6 100644
--- a/challenge-154/paulo-custodio/python/ch-1.py
+++ b/challenge-154/paulo-custodio/python/ch-1.py
@@ -1,4 +1,4 @@
-#!/usr/bin/env perl
+#!/usr/bin/env python3
 
 # Challenge 154
 #
diff --git a/challenge-154/paulo-custodio/python/ch-2.py b/challenge-154/paulo-custodio/python/ch-2.py
index 91384eb9f6..0afb22504f 100644
--- a/challenge-154/paulo-custodio/python/ch-2.py
+++ b/challenge-154/paulo-custodio/python/ch-2.py
@@ -1,4 +1,4 @@
-#!/usr/bin/env perl
+#!/usr/bin/env python3
 
 # Challenge 154
 #
diff --git a/challenge-155/paulo-custodio/perl/ch-1.pl b/challenge-155/paulo-custodio/perl/ch-1.pl
index ff00af24a0..80eb7c1565 100644
--- a/challenge-155/paulo-custodio/perl/ch-1.pl
+++ b/challenge-155/paulo-custodio/perl/ch-1.pl
@@ -2,7 +2,7 @@
 
 # Challenge 155
 #
-# TASK #1 › Fortunate Numbers
+# TASK #1 > Fortunate Numbers
 # Submitted by: Mohammad S Anwar
 # Write a script to produce first 8 Fortunate Numbers (unique and sorted).
 #
diff --git a/challenge-155/paulo-custodio/perl/ch-2.pl b/challenge-155/paulo-custodio/perl/ch-2.pl
index 4ff1516026..fbaa92c2ee 100644
--- a/challenge-155/paulo-custodio/perl/ch-2.pl
+++ b/challenge-155/paulo-custodio/perl/ch-2.pl
@@ -2,7 +2,7 @@
 
 # Challenge 155
 #
-# TASK #2 › Pisano Period
+# TASK #2 > Pisano Period
 # Submitted by: Mohammad S Anwar
 # Write a script to find the period of the 3rd Pisano Period.
 #
diff --git a/challenge-155/paulo-custodio/python/ch-1.py b/challenge-155/paulo-custodio/python/ch-1.py
new file mode 100644
index 0000000000..e1cdaebf76
--- /dev/null
+++ b/challenge-155/paulo-custodio/python/ch-1.py
@@ -0,0 +1,32 @@
+#!/usr/bin/env python3
+
+# Challenge 155
+#
+# TASK #1 > Fortunate Numbers
+# Submitted by: Mohammad S Anwar
+# Write a script to produce first 8 Fortunate Numbers (unique and sorted).
+#
+# According to Wikipedia
+#
+# A Fortunate number, named after Reo Fortune, is the smallest integer m > 1
+# such that, for a given positive integer n, pn# + m is a prime number, where
+# the primorial pn# is the product of the first n prime numbers.
+#
+# Expected Output
+# 3, 5, 7, 13, 17, 19, 23, 37
+
+from math import prod
+from sympy import isprime, nextprime
+
+fortunate = {}
+
+primes = [2]
+while len(fortunate) < 8:
+    p = prod(primes)
+    m = 2
+    while not isprime(p + m):
+        m += 1
+    fortunate[m] = 1
+    primes.append(nextprime(primes[-1]))
+
+print(", ".join(map(str, sorted(fortunate.keys()))))
diff --git a/challenge-155/paulo-custodio/python/ch-2.py b/challenge-155/paulo-custodio/python/ch-2.py
new file mode 100644
index 0000000000..f5408b05db
--- /dev/null
+++ b/challenge-155/paulo-custodio/python/ch-2.py
@@ -0,0 +1,57 @@
+#!/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))