已知有窮數(shù)列
滿足a
i∈{-1,0,1}(i=1,2,?,N).給定正整數(shù)m,若存在正整數(shù)s,t(s≠t),使得對(duì)任意的k∈{0,1,2,?,m-1},都有a
s+k=a
t+k,則稱數(shù)列A是m-連續(xù)等項(xiàng)數(shù)列.
(1)判斷數(shù)列A:1,-1,0,-1,0,-1,1是否是3-連續(xù)等項(xiàng)數(shù)列,并說(shuō)明理由;
(2)若項(xiàng)數(shù)為N的任意數(shù)列A都是2-連續(xù)等項(xiàng)數(shù)列,求N的最小值;
(3)若數(shù)列A:a
1,a
2,?,a
N不是4-連續(xù)等項(xiàng)數(shù)列,而數(shù)列A
1:a
1,a
2,?,a
N,-1,數(shù)列A
2:a
1,a
2,?,a
N,0與數(shù)列A
3:a
1,a
2,?,a
N,1都是4-連續(xù)等項(xiàng)數(shù)列,且a
3=0,求a
N的值.