Step by Step solution about How to resolve the algorithm Jacobsthal numbers step by step in the Julia programming language

This Julia code explores the sequences of Jacobsthal numbers, Jacobsthal-Lucas numbers, oblong Jacobsthal numbers, and Jacobsthal prime numbers. Here's a breakdown of the code:

1. Importing Libraries:

   • using Lazy: This imports the Lazy package for creating lazy sequences.
   • using Primes: This imports the Primes package for working with prime numbers.

2. Defining Functions:

   • J(n): This function computes the Jacobsthal number for index n.
   • L(n): This function computes the Jacobsthal-Lucas number for index n.

3. Creating Lazy Sequences:

   • Jacobsthal: This is a lazy sequence that generates Jacobsthal numbers starting from index 0.
   • JLucas: This is a lazy sequence that generates Jacobsthal-Lucas numbers starting from index 0.
   • Joblong: This is a lazy sequence that generates oblong Jacobsthal numbers starting from index 0.
   • Jprimes: This is a lazy sequence that generates Jacobsthal numbers starting from index 0, filtered to include only prime numbers.

4. Helper Function:

   • printrows: This is a helper function that prints the elements of a given vector in rows, with customizable column size, number of columns, and left/right justification.

5. Printing Sequences:

   • The code uses the printrows function to print the first 30 Jacobsthal numbers, 30 Jacobsthal-Lucas numbers, 20 oblong Jacobsthal numbers, and 15 Jacobsthal prime numbers. The output is formatted with specific column sizes and justification.

Overall, this code demonstrates the use of lazy sequences to efficiently generate and explore different types of Jacobsthal numbers, showcasing the versatility of the Julia programming language for mathematical computations.

using Lazy
using Primes

J(n) = (2^n - (-1)^n) ÷ 3
L(n) =  2^n + (-1)^n

Jacobsthal = @>> Lazy.range(0) map(J)
JLucas = @>> Lazy.range(0) map(L)
Joblong = @>> Lazy.range(big"0") map(n -> J(n) * J(n + 1))
Jprimes = @>> Lazy.range(big"0") map(J) filter(isprime)

function printrows(title, vec, columnsize = 15, columns = 5, rjust=true)
    println(title)
    for (i, n) in enumerate(vec)
        print((rjust ? lpad : rpad)(n, columnsize), i % columns == 0 ? "\n" : "")
    end
    println()
end

printrows("Thirty Jacobsthal numbers:", collect(take(30, Jacobsthal)))
printrows("Thirty Jacobsthal-Lucas numbers:", collect(take(30, JLucas)))
printrows("Twenty oblong Jacobsthal numbers:", collect(take(20, Joblong)))
printrows("Fifteen Jacabsthal prime numbers:", collect(take(15, Jprimes)), 40, 1, false)