problem-049.py

### Problem 49 - Prime Permutations
###------------------------------------------------------------------------------------------------------------------------------------------------------------
### The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways:
### (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
### There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
### What 12-digit number do you form by concatenating the three terms in this sequence?

### Solution

# Function to determine if prime
def isPrime(n: int) -> bool:
    if n < 2:
        return False
    elif n == 2:
        return True
    else:
        i = 2
        while i ** 2 <= n:
            if n % i == 0:
                return False
            i += 1
        return True


# Function to determine if permutation
def isPerm(a: int, b: int) -> bool:
    digits = list()
    for i in str(a):
        digits.append(i)
    for j in str(b):
        if j in digits:
            digits.remove(j)
    return len(digits) == 0


# Generate list of 4-digit primes
primes = []
n = 1000
while True:
    if n > 9999:
        break
    if isPrime(n):
        primes.append(n)
    n += 1

# Generate list of permutations of 4-digit primes
perms = []
for i in range(len(primes)):
    currPerms = [primes[i]]
    for j in range(i, len(primes)):
        if primes[i] == primes[j]:
            continue
        elif isPerm(primes[i], primes[j]):
            currPerms.append(primes[j])
    if len(currPerms) > 2:
        perms.append(currPerms)

# Determine if there is a constant difference in sequence
sequences = []
for i in perms:
    diff = i[1] - i[0]
    const = True
    for j in range(1, len(i) - 1):
        if i[j + 1] - i[j] != diff:
            const = False
            break
    if const == True:
        sequences.append(i)

finalNum = ""
for i in sequences:
    finalNum += str(i)

print(
    "The 12-digit number from concatenating the number sequence is: "
    + finalNum
)