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

The provided Julia code finds and prints the first 400 magnanimous numbers.

Magnanimous Numbers: Magnanimous numbers are positive integers that have the following property: for each digit pair ab in the number, a + b is a prime number. For example, the number 13 is magnanimous because 1 + 3 = 4, which is prime.

Code Explanation:

1. using Primes: This line imports the Primes module, which provides functions for working with prime numbers.

2. ismagnanimous(n) Function:

   • This function checks if a given integer n is magnanimous.
   • It starts by checking if n is less than 10. If it is, n is considered magnanimous.
   • It then iterates through the digits of n from the least significant digit to the most significant digit.
   • For each pair of digits ab, it calculates q + r, where q is the quotient of n divided by 10^i and r is the remainder.
   • It then checks if q + r is prime using the isprime function from the Primes module. If any pair of digits does not satisfy this condition, n is not magnanimous, and the function returns false.
   • If all pairs of digits satisfy the condition, n is magnanimous, and the function returns true.

3. magnanimous(N) Function:

   • This function generates a vector containing the first N magnanimous numbers.
   • It initializes an empty vector mvec and a counter i to 0.
   • It enters a loop that continues until the length of mvec is equal to N.
   • Inside the loop, it checks if i is magnanimous using the ismagnanimous function. If it is, i is added to mvec.
   • Then, it increments i by 1 and repeats the process.

4. Constant mag400:

   • This constant stores the first 400 magnanimous numbers generated by the magnanimous function.

5. Printing Results:

   • The code prints the first 24 magnanimous numbers, followed by the 241st to 250th magnanimous numbers, and finally the 391st to 400th magnanimous numbers.

using Primes

function ismagnanimous(n)
    n < 10 && return true
    for i in 1:ndigits(n)-1
        q, r = divrem(n, 10^i)
        !isprime(q + r) && return false
    end
    return true
end

function magnanimous(N)
    mvec, i = Int[], 0
    while length(mvec) < N
        if ismagnanimous(i)
            push!(mvec, i)
        end
        i += 1
    end
    return mvec
end

const mag400 = magnanimous(400)
println("First 45 magnanimous numbers:\n", mag400[1:24], "\n", mag400[25:45])
println("\n241st through 250th magnanimous numbers:\n", mag400[241:250])
println("\n391st through 400th magnanimous numbers:\n", mag400[391:400])