How to resolve the algorithm Almost prime step by step in the Lua programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Almost prime step by step in the Lua programming language

Table of Contents

Problem Statement

A   k-Almost-prime   is a natural number

n

{\displaystyle n}

that is the product of

k

{\displaystyle k}

(possibly identical) primes.

1-almost-primes,   where

k

1

{\displaystyle k=1}

,   are the prime numbers themselves. 2-almost-primes,   where

k

2

{\displaystyle k=2}

,   are the   semiprimes.

Write a function/method/subroutine/... that generates k-almost primes and use it to create a table here of the first ten members of k-Almost primes for

1 <= K <= 5

{\displaystyle 1<=K<=5}

.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Almost prime step by step in the Lua programming language

Source code in the lua programming language

-- Returns boolean indicating whether n is k-almost prime
function almostPrime (n, k)
    local divisor, count = 2, 0
    while count < k + 1 and n ~= 1 do
        if n % divisor == 0 then
            n = n / divisor
            count = count + 1
        else
            divisor = divisor + 1
        end
    end
    return count == k
end
 
-- Generates table containing first ten k-almost primes for given k
function kList (k)
    local n, kTab = 2^k, {}
    while #kTab < 10 do
        if almostPrime(n, k) then
            table.insert(kTab, n)
        end
        n = n + 1
    end
    return kTab
end

-- Main procedure, displays results from five calls to kList()
for k = 1, 5 do
    io.write("k=" .. k .. ": ")
    for _, v in pairs(kList(k)) do
        io.write(v .. ", ")
    end
    print("...")
end


  

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