Data commit

Task/Rare-numbers/Python/rare-numbers-1.py

@@ -0,0 +1,35 @@
+# rare.py
+# find rare numbers
+# by kHz
+
+from math import floor, sqrt
+from datetime import datetime
+
+def main():
+	start = datetime.now()
+	for i in xrange(1, 10 ** 11):
+		if rare(i):
+			print "found a rare:", i
+	end = datetime.now()
+	print "time elapsed:", end - start
+
+def is_square(n):
+	s = floor(sqrt(n + 0.5))
+	return s * s == n
+
+def reverse(n):
+	return int(str(n)[::-1])
+
+def is_palindrome(n):
+	return n == reverse(n)
+
+def rare(n):
+	r = reverse(n)
+	return (
+		not is_palindrome(n) and
+		n > r and
+		is_square(n+r) and is_square(n-r)
+	)
+
+if __name__ == '__main__':
+	main()

Task/Rare-numbers/Python/rare-numbers-2.py

@@ -0,0 +1,64 @@
+# rare.py
+# by xing216
+
+import time as t
+from functools import cache
+
+@cache
+def isSquare(n: int) ->bool:
+    if n < 0:
+        return False
+    if n == 0:
+        return True
+    while n&3 == 0:
+        n=n>>2
+    if n&7 != 1:
+        return False
+    if n==1:
+        return True
+    c = n%10
+    if c in {3, 7}:
+        return False
+    if n % 7 in {3, 5, 6}:
+        return False
+    if n % 9 in {2,3,5,6,8}:
+        return False
+    if n % 13 in {2,5,6,7,8,11}:
+        return False
+    if c == 5:
+        if (n//10)%10 != 2:
+            return False
+        if (n//100)%10 not in {0,2,6}:
+            return False
+        if (n//100)%10 == 6:
+            if (n//1000)%10 not in {0,5}:
+                return False
+    else:
+        if (n//10)%4 != 0:
+            return False
+    s = (len(str(n))-1) // 2
+    x = (10**s) * 4
+    A = {x, n}
+    while x * x != n:
+        x = (x + (n // x)) >> 1
+        if x in A:
+            return False
+        A.add(x)
+    return True
+
+@cache
+def main() -> None:
+    r = 1
+    start = t.time()
+    while True:
+        strr = str(r)
+        if int(strr[0]) % 2 != 0:
+            r += int('1' + (len(strr)-1)*'0' )
+        r1 = int(strr[::-1])
+        x = r + r1
+        y = r - r1
+        if isSquare(x) and isSquare(y) and r != r1:
+            print(f'success:  {r} ~{t.time()-start}s')
+        r+=1
+if __name__ == '__main__':
+    main()