Pell numbers: Difference between revisions
Added Python implementation for Pell numbers task
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=={{header|Python}}==
<syntaxhighlight lang="python3">
# 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}")
</syntaxhighlight>
{{out}}
<pre style="height: 15em;">
The first 10 Pell Numbers:
0 1 2 5 12 29 70 169 408 985
The first 10 Pell-Lucas Numbers:
2 2 6 14 34 82 198 478 1154 2786
The first 10 rational and decimal approximations of sqrt(2) (1.4142135624):
rational | decimal
1/1 ≈ 1.0000000000
3/2 ≈ 1.5000000000
7/5 ≈ 1.4000000000
17/12 ≈ 1.4166666667
41/29 ≈ 1.4137931034
99/70 ≈ 1.4142857143
239/169 ≈ 1.4142011834
577/408 ≈ 1.4142156863
1393/985 ≈ 1.4142131980
3363/2378 ≈ 1.4142136249
The first 7 Pell Primes:
index | Pell Prime
2 | 2
3 | 5
5 | 29
11 | 5741
13 | 33461
29 | 44560482149
41 | 1746860020068409
The first 10 Newman-Shank-Williams numbers:
1 7 41 239 1393 8119 47321 275807 1607521 9369319
The first 10 near isosceles right triangles:
(3, 4, 5)
(20, 21, 29)
(119, 120, 169)
(696, 697, 985)
(4059, 4060, 5741)
(23660, 23661, 33461)
(137903, 137904, 195025)
(803760, 803761, 1136689)
(4684659, 4684660, 6625109)
(27304196, 27304197, 38613965)
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=={{header|Quackery}}==
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