Lucas number algorithm

lucas.py

@@ -79,8 +79,44 @@ def Jacobi(a, n):
         return -1 * Jacobi(n, a)
     return Jacobi(n, a)
 
+def FirstD(n):
+    """Return first D in the sequence 5, -7, 9, -11, 13, -15... for which the
+    Jacobi symbol (D/n) is -1
+    """
+    if hasIntSQRT(n):
+        raise ValueError("n must not be a square")
+    if n < 1 or n % 2 == 0:
+        raise ValueError("n must be a positive odd number")
+    for D in Dsequence():
+        if Jacobi(D/n) == -1:
+            return D
+    # Shouldn't fire
+    return 0
+
+def Lucas(n, p, q):
+    """Function for generating values of a lucas sequence with parameters p, q.
+    Via formula at <https://en.wikipedia.org/wiki/Lucas_sequence>
+    """
+    if n < 0:
+        raise ValueError("n must be a non-negative integer")
+    if n == 0:
+        return 0, 2
+    Unm1, Vnm1 = Lucas(n - 1, p, q)
+    Un = (p * Unm1 + Vnm1) // 2
+    Vn = ((p * p - 4 * q) * Unm1 + p * Vnm1) // 2
+    return Un, Vn
+
+def LucasUn(n, p, q):
+    """Return only the U numbers from a lucas sequence Un(P, Q). For example if
+    P = 1, and Q = -1 this will return the Fibonacci numbers; if P = 3 and Q =
+    2 then it returns the Mersenne numbers etc.
+    """
+    return Lucas(n, p, q)[0]
 
-
+def LucasVn(n, p, q):
+    """Return only V numbers from a local sequence Vn(P, Q).
+    """
+    return Lucas(n, p, q)[1]