## Exercice 1

def f(n):
    return (n**2+1)%10**4

print(f(12345))

N=1990

for k in range(100):
    N=f(N)
    print(N)


## Exercice 2

def estcarre(x):
    y=int(x**(1/2))
    return y*y==x

for n in range(1,10000):
    N = n**2+(n+1)**2
    if estcarre(N):
        k = int(N**0.5)
        print( (n, n+1, k) )
        print(k/n)


## Exercice 3

def isprime(n):
    for k in range(2,int(n**0.5)+1):
        if n%k==0:
            return False
    return True


for n in range(100):
    if isprime(n):
        print(n)

nbchiffres_max = 50

chiffres = "0123456789"

L=[[2,3,5,7]]

for k in range(nbchiffres_max):
    H=[]
    for nombre in L[-1]:
        for c in chiffres:
            n = int(str(nombre)+c)
            if isprime(n):
                H.append(n)
    L.append(H)

for k in range(len(L)):
    print(L[k])


## Exercice 4

import matplotlib.pyplot as plt
import numpy as np

S=4
X,Y=[],[]
for k in range(S):
    X.append([np.cos(2*k*np.pi/S)])
    Y.append([np.sin(2*k*np.pi/S)])

N=1000
r=0.01

for n in range(N):
    for k in range(S-1):
        X[k].append(X[k][-1]+r*(X[k+1][-1]-X[k][-1]))
        Y[k].append(Y[k][-1]+r*(Y[k+1][-1]-Y[k][-1]))
    X[-1].append(X[-1][-1]+r*(X[0][-1]-X[-1][-1]))
    Y[-1].append(Y[-1][-1]+r*(Y[0][-1]-Y[-1][-1]))


for k in range(S):
    plt.plot(X[k],Y[k])

plt.axis("equal")
plt.show()



## Exercice 5

def voisins(p):
    x,y=p[0],p[1]
    return [(x-1,y),(x+1,y),(x-0.5,y-1),(x-0.5,y+1),(x+0.5,y-1),(x+0.5,y+1)]

def nb_voisins_flocons(p,F):
    V=voisins(p)
    c=0
    for v in V:
        if v in F:
            c+=1
    return c

def croissance(F):
    C=[]
    for f in F:
        V=voisins(f)
        for v in V:
            if not(v in C) and nb_voisins_flocons(v,F)==1:
                C.append(v)
    return C

F=[(0,0)]

for k in range(28):
    F+=croissance(F)

X,Y=[],[]
for f in F:
    X.append(f[0])
    Y.append(f[1])

import matplotlib.pyplot as plt

plt.scatter(X,Y)
plt.axis("equal")
plt.show()