igorvanloo

def compute(cipher):
    possiblecodes = []
    for x in range(97,123):
        for y in range(97, 123):
            for z in range(97,123):
                password = chr(x) + chr(y) + chr(z)
                count = 0
                decrypt = []
                for i in cipher:
                    temp = i^(ord(password[count % 3]))

igorvanloo

def compute():
    count = []
    for n in range(1,10):
        for i in range(1,22):
            if i == len(str(n**i)):
                count.append(n**i) 
    return len(count)
  
#Used the following function to find the bounds for n
#n = 9 bound is 22 because 9^22

igorvanloo

def compute(limit):
    f = [int(4*(x**2)+1) for x in range(limit+1)] #Initialise the list f 
    max_prime_factor = [0]*(limit+1) #Initialise the list max_prime_factor
    for x in range(1,len(f)): #Go through f
        div = f[x] #Initialise divisor
        if div > 1: #Check if divisor > 1
            curr1 = x % div
            while curr1 <= limit: #while curr = x + k*f[x] < limit we continue
                if f[curr1] % div == 0: #Check if f[x+k*f[x]] is divisible by f[x]
                    max_prime_factor[curr1] = max(max_prime_factor[curr1], div)

igorvanloo

def compute():
    eulercoins = [1504170715041707]
    current_eulercoin = 1504170715041707
    inv = pow(1504170715041707, -1, 4503599627370517)
    n = 2
    while True:
        number = 1504170715041707*n % 4503599627370517 #Search downwards
        if number < current_eulercoin:
            current_eulercoin = number
            eulercoins.append(number)

igorvanloo

def A(k,n):
    total = 0
    f0 = 1
    modulo = 1000000007
    power = pow(2, n//k, modulo)
    for a in range(0, n//k + 1):
        total = (total + (f0 * pow(power, k-2*a, modulo))) % modulo
        f0 = (f0*(k-2*a)*(k-2*a-1)) % modulo
        f0 = (f0*pow((a+1)**2, -1, modulo)) % modulo
    return total

igorvanloo

def compute():    
    matrix = [[131, 673, 234, 103,18],
              [201, 96, 342, 965, 150],
              [630, 803, 746, 422, 111],
              [537, 699, 497, 121, 956],
              [805, 732, 524, 37, 331]]
    
    rows = len(matrix)      #Number of rows
    columns = len(matrix[0])#Number of columns
    

igorvanloo

def compute(limit):
    d = [1] + [0] * limit
    primes = eulerlib.primes(limit)
    mod = 10**9
    Fibonnaci_numbers = [2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368]

    for p in primes:
        for i in range(p,limit+1):
            d[i] += (p*d[i-p] % mod)
    

igorvanloo

def is_cyclic(x,y):
    if (x % 100) == int(str(y // 100)):
        return True
    return False

def compute():
    tri = [(int(x*(x + 1)/2), "triangle") for x in range(1,1000) if 999 < x*(x + 1)/2 < 10000]
    sq = [(int(x*(x)), "square") for x in range(1,1000) if 999 < x*(x) < 10000]
    pen = [(int(x*(3*x - 1)/2), "pentagonal") for x in range(1,1000) if 999 < x*(3*x - 1)/2 < 10000]
    hexa = [(int(x*(2*x - 1)), "hexagonal") for x in range(1,1000) if 999 < (x*(2*x - 1)) < 10000]

igorvanloo

def PentagonalNumberTheorem(N):
    p = [1] + [0]*(N + 1) #Initalise array
        
    for n in range(1,len(p)):
        y = 1
        while True:            
            if y % 2 == 0: #Find sign
                sign = -1
            else:
                sign = 1

igorvanloo

def dicecomb(): #Produces all dice combinations, there are 10 C 6 = 210
    dicecombs = set()
    for a in range(0,10):
        for b in range(0,9):
            for c in range(0,8):
                for d in range(0,7):
                    for e in range(0,6):
                        for f in range(0,5):
                            if len(set([a,b,c,d,e,f])) == 6:
                                dicecombs.add(tuple(sorted((a,b,c,d,e,f))))