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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