Chernick's Carmichael numbers: Difference between revisions
Realize in F#
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* [https://oeis.org/A318646 OEIS A318646: The least Chernick's "universal form" Carmichael number with n prime factors]
=={{header|F_Sharp|F#}}==
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_function Extensible Prime Generator (F#)]
<lang fsharp>
// Generate Chernick's Carmichael numbers. Nigel Galloway: June 1st., 2019
let fN g=let mx=int(sqrt(float g)) in pCache|>Seq.takeWhile(fun n->n<=mx)|>Seq.forall(fun n->g%(int64 n)>0L)
let fMk m k=fN (6L*m+1L) && fN (12L*m+1L) && [1..k-2]|>List.forall(fun n->fN (9L*(pown 2L n)*m+1L))
let fX k=Seq.initInfinite(fun n->int64(n+1)*(pown 2L (k-4))) |> Seq.filter(fun n->fMk n k )
let cherCar k=let m=Seq.head(fX k) in printfn "cherCar(%d): m=%d primes -> %A " k m ([6L*m+1L;12L*m+1L]@List.init(k-2)(fun n->9L*(pown 2L (n+1))*m+1L))
[4..9] |> Seq.iter cherCar
</lang>
{{out}}
<pre>
cherCar(4): m=1 primes -> [7L; 13L; 19L; 37L]
cherCar(5): m=380 primes -> [2281L; 4561L; 6841L; 13681L; 27361L]
cherCar(6): m=380 primes -> [2281L; 4561L; 6841L; 13681L; 27361L; 54721L]
cherCar(7): m=780320 primes -> [4681921L; 9363841L; 14045761L; 28091521L; 56183041L; 112366081L; 224732161L]
cherCar(8): m=950560 primes -> [5703361L; 11406721L; 17110081L; 34220161L; 68440321L; 136880641L; 273761281L; 547522561L]
cherCar(9): m=950560 primes -> [5703361L; 11406721L; 17110081L; 34220161L; 68440321L; 136880641L; 273761281L; 547522561L; 1095045121L]
</pre>
=={{header|Go}}==
<lang go>package main
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