對(duì)于每項(xiàng)均是正整數(shù)的數(shù)列A：a1,a2,a3,…,an,
定義變換T1,T1將數(shù)列A變換為數(shù)列T1(A)：n,a1－1,a2－1,…,an－1
對(duì)于每項(xiàng)均是非負(fù)整數(shù)的數(shù)列B：b1,b2,b3,…,bm,
定義變換T2 ,T2將數(shù)列B各項(xiàng)從大到小排列,然后去掉所有為零的項(xiàng),得到數(shù)列T2(B).
又定義S(B)=2(b1+2b2+3b3+…+mbm)+ b12+b22+b32+…+bm2
設(shè)A0是每項(xiàng)均為正整數(shù)的有窮數(shù)列,令A(yù)K+1=T2(T1Ak)),(k=0,1,2…)
1）如果數(shù)列A0為5,3,2；寫出數(shù)列A1,A2
2）對(duì)于每項(xiàng)均是正整數(shù)的有窮數(shù)列A,證明S（T1（A））=S（A）
3）證明對(duì)于任意給定的每項(xiàng)均是正整數(shù)的有窮數(shù)列A0,存在正整數(shù)K,
當(dāng)k K時(shí),S（Ak+1）=S（Ak）.