Solve Joseph’s Cousin in python

solutions/beecrowd/1032/1032.py

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+import sys
+from math import sqrt
+
+sys.setrecursionlimit(3505)
+
+primes = {
+    2: 3,
+    3: 5,
+    5: 7,
+    7: 11,
+    11: 13,
+    13: 17,
+    17: 19,
+    19: 23,
+    23: 29,
+    29: 31,
+    31: 37,
+    37: 41,
+    41: 43,
+    43: 47,
+    47: 53,
+    53: 59,
+    59: 61,
+    61: 67,
+    67: 71,
+    71: 73,
+    73: 79,
+    79: 83,
+    83: 89,
+    89: 97,
+    97: 101,
+}
+
+
+def is_prime(number):
+    if number == 2:
+        return True
+    if number <= 1 or number % 2 == 0:
+        return False
+    for divisor in range(3, int(sqrt(number)) + 1, 2):
+        if number % divisor == 0:
+            return False
+    return True
+
+
+def next_prime(number):
+    if number in primes:
+        return primes[number]
+
+    next = number + 1
+    while not is_prime(next):
+        next += 1
+    primes[number] = next
+
+    return primes[number]
+
+
+def josephus(n, k=2) -> int:
+    if n == 1:
+        return 1
+    return ((josephus(n - 1, next_prime(k)) + k - 1) % n) + 1
+
+
+for line in sys.stdin:
+    n = int(line)
+
+    if n == 0:
+        break
+
+    print(josephus(n))

solutions/beecrowd/1032/generate_in.sh

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+#!/usr/bin/env bash
+
+set -euo pipefail
+
+seq 3501
+echo 0