58 lines
1.9 KiB
Python
58 lines
1.9 KiB
Python
# 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}")
|