Legendere symbol; start Jacobi

lucas.py

@@ -1,5 +1,5 @@
 # Finding lucas pseudoprimes
-from math import sqrt
+from math import sqrt, gcd
 
 def isqrt(n):
     """ Find the integer square root of n via newton's method, code via
@@ -21,4 +21,48 @@ def hasIntSQRT(n):
     isq = isqrt(n)
     return isq * isq == n
 
+def Dsequence():
+    """Generate sequence 5, -7, 9, -11, 13, -15...
+    """
+    val = 5
+    while True:
+        if val % 4 == 1:
+            yield val
+        else:
+            yield -val
+        val = val + 2
+
+def Legendere(a, p):
+    if (p % 2 == 0):
+        raise ValueError("p must be odd, is {}".format(p))
+    lv =  pow(a, (p-1)//2, p)
+    if lv == p - 1:
+        lv = -1
+    return lv
+
+def Jacobi(a, n):
+    if (n % 2 == 0):
+        raise ValueError("n must be odd, is {}".format(n))
+    a = a % n
+    mv = 1
+    if (a % 2 == 0):
+        a = a // 2
+        nm8 = n % 8
+        if (nm8 == 3 or nm8 == 5):
+            mv = -1
+    if n == 1:
+        return mv * 1
+    if gcd(a, n) != 1:
+        return 0
+    return mv * Jacobi(n, a)
+
+for n in range(1, 21, 2):
+    print("{}:\t{}".format(n, Jacobi(3, n)))
+
+
+
+
+
+
+