Cullen and Woodall numbers: Difference between revisions
Add Scala implementation
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First 12 Woodall primes (in terms of n):
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="PARI/GP">
/* Define the Cullen and Woodall number functions */
cullen(n) = n * 2^n + 1;
woodall(n) = n * 2^n - 1;
{
/* Generate the first 20 Cullen and Woodall numbers */
print(vector(20, n, cullen(n)));
print(vector(20, n, woodall(n)));
/* Find the first 5 Cullen prime numbers */
cps = [];
for(i = 1, +oo,
if(isprime(cullen(i)),
cps = concat(cps, i);
if(#cps >= 5, break);
);
);
print(cps);
/* Find the first 12 Woodall prime numbers */
wps = [];
for(i = 1, +oo,
if(isprime(woodall(i)),
wps = concat(wps, i);
if(#wps >= 12, break);
);
);
print(wps);
}
</syntaxhighlight>
{{out}}
<pre>
[3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521]
[1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519]
[1, 141, 4713, 5795, 6611]
[2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462]
</pre>
Line 1,506 ⟶ 1,547:
First 12 Woodall primes in terms of n:
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
=={{header|Scala}}==
{{trans|Java}}
<syntaxhighlight lang="Scala">
import java.math.BigInteger
import scala.annotation.tailrec
object CullenAndWoodhall extends App {
val Certainty = 20
var number: BigInteger = _
var power: BigInteger = _
var count: Int = _
var primeIndex: Int = _
sealed trait NumberType
case object Cullen extends NumberType
case object Woodhall extends NumberType
numberSequence(20, Cullen)
numberSequence(20, Woodhall)
primeSequence(5, Cullen)
primeSequence(12, Woodhall)
def numberSequence(aCount: Int, aNumberType: NumberType): Unit = {
println(s"\nThe first $aCount $aNumberType numbers are:")
numberInitialise()
(1 to aCount).foreach { _ =>
print(nextNumber(aNumberType).toString + " ")
}
println()
}
def primeSequence(aCount: Int, aNumberType: NumberType): Unit = {
println(s"\nThe indexes of the first $aCount $aNumberType primes are:")
primeInitialise()
@tailrec
def findPrimes(): Unit = {
if (count < aCount) {
if (nextNumber(aNumberType).isProbablePrime(Certainty)) {
print(primeIndex + " ")
count += 1
}
primeIndex += 1
findPrimes()
}
}
findPrimes()
println()
}
def nextNumber(aNumberType: NumberType): BigInteger = {
number = number.add(BigInteger.ONE)
power = power.shiftLeft(1)
aNumberType match {
case Cullen => number.multiply(power).add(BigInteger.ONE)
case Woodhall => number.multiply(power).subtract(BigInteger.ONE)
}
}
def numberInitialise(): Unit = {
number = BigInteger.ZERO
power = BigInteger.ONE
}
def primeInitialise(): Unit = {
count = 0
primeIndex = 1
numberInitialise()
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 20 Cullen numbers are:
3 9 25 65 161 385 897 2049 4609 10241 22529 49153 106497 229377 491521 1048577 2228225 4718593 9961473 20971521
The first 20 Woodhall numbers are:
1 7 23 63 159 383 895 2047 4607 10239 22527 49151 106495 229375 491519 1048575 2228223 4718591 9961471 20971519
The indexes of the first 5 Cullen primes are:
1 141 4713 5794 6611
The indexes of the first 12 Woodhall primes are:
2 3 6 30 75 81 115 123 249 362 384 462
</pre>
Line 1,565 ⟶ 1,697:
{{libheader|Wren-big}}
Cullen primes limited to first 2 as very slow after that.
<syntaxhighlight lang="
var cullen = Fn.new { |n| (BigInt.one << n) * n + 1 }
Line 1,620 ⟶ 1,752:
{{libheader|Wren-gmp}}
Cullen primes still slow to emerge, just over 10 seconds overall.
<syntaxhighlight lang="
import "./gmp" for Mpz
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