Cullen and Woodall numbers: Difference between revisions

=={{header|Julia}}==

<lang julia>using Lazy

using Primes

cullen(n, two = BigInt(2)) = n * two^n + 1

woodall(n, two = BigInt(2)) = n * two^n - 1

primecullens = @>> Lazy.range() filter(n -> isprime(cullen(n)))

primewoodalls = @>> Lazy.range() filter(n -> isprime(woodall(n)))

#primewoodalls(n)

println("First 20 Cullen numbers: ( n × 2**n + 1)\n", [cullen(n, 2) for n in 1:20]) # A002064

println("First 20 Woodall numbers: ( n × 2**n - 1)\n", [woodall(n, 2) for n in 1:20]) # A003261

println("\nFirst 5 Cullen primes: (in terms of n)\n", take(5, primecullens)) # A005849

println("\nFirst 12 Woodall primes: (in terms of n)\n", Int.(collect(take(12, primewoodalls)))) # A002234

</lang>{{out}}

<pre>

First 20 Cullen numbers: ( n × 2**n + 1)

[3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521]

First 20 Woodall numbers: ( n × 2**n - 1)

[1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519]

First 5 Cullen primes: (in terms of n)

List: (1 141 4713 5795 6611)

First 12 Woodall primes: (in terms of n)

[2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462]

</pre>