Attention : ne pas oublier d'exécuter la première cellule !
nom="u"
nmin=0
u_nmin=3
def f(n) :
return 2*n+1
print(f"{nom}_{nmin} = {u_nmin} et pour tout n>={nmin}, {nom}_n+1 = f({nom}_n).")
u_0 = 3 et pour tout n>=0, u_n+1 = f(u_n).
n=nmin
u=u_nmin
while(n<=10):
print(f"{nom}_{n:2d} = {u:4d}")
n=n+1
u=f(u)
u_ 0 = 3 u_ 1 = 7 u_ 2 = 15 u_ 3 = 31 u_ 4 = 63 u_ 5 = 127 u_ 6 = 255 u_ 7 = 511 u_ 8 = 1023 u_ 9 = 2047 u_10 = 4095
n=nmin
u=u_nmin
s=u
while(n<=10):
print(f"{nom}_{n:2d} = {u:4d} S_{n:2d} = {s:4d}")
n=n+1
u=f(u)
s=s+u
u_ 0 = 3 S_ 0 = 3 u_ 1 = 7 S_ 1 = 10 u_ 2 = 15 S_ 2 = 25 u_ 3 = 31 S_ 3 = 56 u_ 4 = 63 S_ 4 = 119 u_ 5 = 127 S_ 5 = 246 u_ 6 = 255 S_ 6 = 501 u_ 7 = 511 S_ 7 = 1012 u_ 8 = 1023 S_ 8 = 2035 u_ 9 = 2047 S_ 9 = 4082 u_10 = 4095 S_10 = 8177
n=nmin
u=u_nmin
while(u<100):
print(f"{nom}_{n:2d} = {u:4d}")
n=n+1
u=f(u)
print("\n------------------\n")
print(f"{nom}_{n:2d} = {u:4d}")
u_ 0 = 3 u_ 1 = 7 u_ 2 = 15 u_ 3 = 31 u_ 4 = 63 ------------------ u_ 5 = 127
n=nmin
u=u_nmin
s=u
while(s<1_000):
print(f"{nom}_{n:2d} = {u:4d} S_{n:2d} = {s:4d}")
n=n+1
u=f(u)
s=s+u
print("\n------------------\n")
print(f"{nom}_{n:2d} = {u:4d} S_{n:2d} = {s:4d}")
u_ 0 = 3 S_ 0 = 3 u_ 1 = 7 S_ 1 = 10 u_ 2 = 15 S_ 2 = 25 u_ 3 = 31 S_ 3 = 56 u_ 4 = 63 S_ 4 = 119 u_ 5 = 127 S_ 5 = 246 u_ 6 = 255 S_ 6 = 501 ------------------ u_ 7 = 511 S_ 7 = 1012