Solve 293 and 686

python/e686.py

@@ -0,0 +1,29 @@
+def p(leading_digits, count):
+    n_cutoff = 18
+    leading_digits_str = str(leading_digits)
+    n_digits = len(leading_digits_str)
+    j, current_leading, found = 1, 2, 0
+
+    while found < count:
+        current_leading *= 2
+        j += 1
+        current_leading_str = str(current_leading)
+        if  current_leading_str[:n_digits] == leading_digits_str:
+            found += 1
+        current_leading = int(current_leading_str[:n_cutoff])
+    return j
+
+
+def euler_686():
+    assert p(12, 1) == 7
+    assert p(12, 2) == 80
+    assert p(123, 45) == 12710
+    assert p(123, 100) == 28343
+    assert p(123, 1000) == 284168
+    return p(123, 678910)
+
+
+if __name__ == "__main__":
+    solution = euler_686()
+    print("e686.py: " + str(solution))
+    assert solution == 193060223