Pell numbers: Difference between revisions
Created Nim solution.
(Created Nim solution.) |
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{{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}}</pre>
=={{header|Nim}}==
<syntaxhighlight lang="Nim">import std/[strformat, strutils, sugar]
import integers
template isOdd(n: int): bool = (n and 1) != 0
iterator pellSequence[T](first, second: T; lim = -1): (int, T) =
## Yield the sucessive values of a Pell or Pell-Lucas sequence
## preceded by their rank.
## If "lim" is specified and greater than 2, only the "lim" first
## values are computed.
## The iterator works with "int" values or "Integer" values.
var prev = first
var curr = second
yield (0, prev)
yield (1, curr)
var count = 2
while true:
swap prev, curr
curr += 2 * prev
yield (count, curr)
inc count
if count == lim: break
echo "First 10 Pell numbers:"
let p = collect:
for (idx, val) in pellSequence(0, 1, 11): val
echo p[0..9].join(" ")
echo "\nFirst 10 Pell-Lucas numbers:"
let q = collect:
for (idx, val) in pellSequence(2, 2, 11): val
echo q[0..9].join(" ")
echo "\nFirst 10 rational approximations of √2:"
for i in 1..10:
let n = q[i] div 2
let d = p[i]
let r = &"{n}/{d}"
echo &"{r:>9} = {n/d:.17}"
echo "\nFirst 10 Pell primes:"
# To avoid an overflow, we need to use Integer values here.
var indices: seq[int]
var count = 0
for (idx, p) in pellSequence(newInteger(0), newInteger(1)):
if p.isPrime:
echo p
indices.add idx
inc count
if count == 10: break
echo "\nFirst 10 Pell primes indices:"
echo indices.join(" ")
echo "\nFirst 10 Newman-Shank-Williams numbers:"
count = 0
var prev: int
for (idx, p) in pellSequence(0, 1):
if idx.isOdd:
inc count
stdout.write prev + p
if count == 10: break
stdout.write ' '
else:
prev = p
echo()
echo "\nFirst 10 near isosceles right triangles:"
count = 0
var sum = 0
for (idx, p) in pellSequence(0, 1):
if idx.isOdd and sum != 0:
echo (sum, sum + 1, p)
inc count
if count == 10: break
inc sum, p
</syntaxhighlight>
{{out}}
<pre>First 10 Pell numbers:
0 1 2 5 12 29 70 169 408 985
First 10 Pell-Lucas numbers:
2 2 6 14 34 82 198 478 1154 2786
First 10 rational approximations of √2:
1/1 = 1.0000000000000000
3/2 = 1.5000000000000000
7/5 = 1.3999999999999999
17/12 = 1.4166666666666667
41/29 = 1.4137931034482758
99/70 = 1.4142857142857144
239/169 = 1.4142011834319526
577/408 = 1.4142156862745099
1393/985 = 1.4142131979695431
3363/2378 = 1.4142136248948696
First 10 Pell primes:
2
5
29
5741
33461
44560482149
1746860020068409
68480406462161287469
13558774610046711780701
4125636888562548868221559797461449
First 10 Pell primes indices:
2 3 5 11 13 29 41 53 59 89
First 10 Newman-Shank-Williams numbers:
1 7 41 239 1393 8119 47321 275807 1607521 9369319
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)
</pre>
=={{header|Perl}}==
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