Merge pull request #10906 from pauloscustodio/master

Add Python solutions

2 files changed, 79 insertions, 0 deletions

diff --git a/challenge-147/paulo-custodio/python/ch-1.py b/challenge-147/paulo-custodio/python/ch-1.py
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+++ b/challenge-147/paulo-custodio/python/ch-1.py
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+#!/usr/bin/env python3
+
+# Challenge 147
+#
+# TASK #1 > Truncatable Prime
+# Submitted by: Mohammad S Anwar
+# Write a script to generate first 20 left-truncatable prime numbers in base 10.
+#
+# In number theory, a left-truncatable prime is a prime number which, in a given
+# base, contains no 0, and if the leading left digit is successively removed,
+# then all resulting numbers are primes.
+#
+# Example
+# 9137 is one such left-truncatable prime since 9137, 137, 37 and 7 are all
+# prime numbers.
+
+from sympy import isprime, nextprime
+
+def left_truncatable_prime_it():
+    prime = None
+    while True:
+        prime = nextprime(prime) if prime is not None else 2
+        if is_left_truncatable_prime(prime):
+            yield prime
+
+def is_left_truncatable_prime(p):
+    while True:
+        if not isprime(p):
+            return False
+        p = int(str(p)[1:]) if len(str(p)) > 1 else ''
+        if p == '':
+            return True
+
+it = left_truncatable_prime_it()
+out = [next(it) for _ in range(20)]
+print(", ".join(map(str, out)))
diff --git a/challenge-147/paulo-custodio/python/ch-2.py b/challenge-147/paulo-custodio/python/ch-2.py
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+++ b/challenge-147/paulo-custodio/python/ch-2.py
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+#!/usr/bin/env python3
+
+# Challenge 147
+#
+# TASK #2 > Pentagon Numbers
+# Submitted by: Mohammad S Anwar
+# Write a script to find the first pair of Pentagon Numbers whose sum and
+# difference are also a Pentagon Number.
+#
+# Pentagon numbers can be defined as P(n) = n(3n - 1)/2.
+#
+# Example
+# The first 10 Pentagon Numbers are:
+# 1, 5, 12, 22, 35, 51, 70, 92, 117 and 145.
+#
+# P(4) + P(7) = 22 + 70 = 92 = P(8)
+# but
+# P(4) - P(7) = |22 - 70| = 48 is not a Pentagon Number.
+
+limit = 100_000_000
+
+pentagon = [1]
+is_pentagon = {}
+
+def find_pair():
+    is_pentagon_func(limit)  # build pentagon up to N
+    try_ = pentagon.copy()
+    for a in try_:
+        for b in try_:
+            if is_pentagon_func(a + b) and is_pentagon_func(abs(a - b)):
+                return a, b
+    raise Exception("No pair found")
+
+def is_pentagon_func(num):
+    while pentagon[-1] < num:
+        n = len(pentagon) + 1
+        p = n * (3 * n - 1) // 2
+        pentagon.append(p)
+        is_pentagon[p] = True
+    return is_pentagon.get(num, False)
+
+a, b = find_pair()
+print(f"({a},{b})")