TP INFO Hors

u0∈N
n∈N
un+1 =(un/2un,
3un+ 1 un
un
n
(un)
u0n∈Nun= 1
u0
4,2,1,4,2,1,4,2,1, . . .
•n
un= 1
•
u0≤100

n
•
•
•
n
1 1000
n
sn=
n
X
k=0
1
n
k.
lim(sn) = 2

........................
n
n
4
'
`nn
`1= 1, `2= 2, `3= 2, `4= 4, `5= 6, . . .
lim `n+1
`n=λ λ ≤1,303577269...

2
•4k+ 1 A
•4k−1B
A B
A B
A= [A1, A2, . . . , AN]B=
[B1, B2, . . . , BN]AnBnn≤N
An= Card({k∈[[1, n]] : 4k+ 1 })
Bn= Card({k∈[[1, n]] : 4k−1})
n∈N
n
124 + 421 = 545.
1293 + 3921 = 5214
5214 + 4125 = 9339.

100
196
n= 196
n∈N
n= 426712
4×2×6×7×1×2 = 672
6×7×2 = 84
8×4 = 32
3×2 = 6
426712 4
n= 277777788888899