Data update

Task/Pell-numbers/Python/pell-numbers.py

@@ -0,0 +1,57 @@
+# pell_numbers.py by Xing216
+def is_prime(n):
+    if n == 1:
+        return False
+    i = 2
+    while i*i <= n:
+        if n % i == 0:
+            return False
+        i += 1
+    return True
+def pell(p0: int,p1: int,its: int):
+    nums = [p0,p1]
+    primes = {}
+    idx = 2
+    while len(nums) != its:
+        p = 2*nums[-1]+nums[-2]
+        if is_prime(p):
+           primes[idx] = p
+        nums.append(p)
+        idx += 1
+    return nums, primes
+def nsw(its: int,pell_nos: list):
+    nums = []
+    for i in range(its):
+        nums.append(pell_nos[2*i] + pell_nos[2*i+1])
+    return nums
+def pt(its: int, pell_nos: list):
+    nums = []
+    for i in range(1,its+1):
+        hypot = pell_nos[2*i+1]
+        shorter_leg = sum(pell_nos[:2*i+1])
+        longer_leg = shorter_leg + 1
+        nums.append((shorter_leg,longer_leg,hypot))
+    return nums
+pell_nos, pell_primes = pell(0,1,50)
+pell_lucas_nos, pl_primes = pell(2,2,10)
+nsw_nos = nsw(10, pell_nos)
+pythag_triples = pt(10, pell_nos)
+sqrt2_approx = {}
+for idx, pell_no in enumerate(pell_nos):
+    numer = pell_nos[idx-1] + pell_no
+    if pell_no != 0:
+        sqrt2_approx[f"{numer}/{pell_no}"] = numer/pell_no
+print(f"The first 10 Pell Numbers:\n {' '.join([str(_) for _ in pell_nos[:10]])}")
+print(f"The first 10 Pell-Lucas Numbers:\n {' '.join([str(_) for _ in pell_lucas_nos])}")
+print(f"The first 10 rational and decimal approximations of sqrt(2) ({(2**0.5):.10f}):")
+print("  rational | decimal")
+for rational in list(sqrt2_approx.keys())[:10]:
+    print(f"{rational:>10} ≈ {sqrt2_approx[rational]:.10f}")
+print("The first 7 Pell Primes:")
+print(" index | Pell Prime")
+for idx, prime in pell_primes.items():
+    print(f"{idx:>6} | {prime}")
+print(f"The first 10 Newman-Shank-Williams numbers:\n {' '.join([str(_) for _ in nsw_nos])}")
+print(f"The first 10 near isosceles right triangles:")
+for i in pythag_triples:
+    print(f" {i}")