已知數(shù)列{an},如果數(shù)列{bn}滿足b1=a1 ,bn=an+an-1 (n≥2,n∈N*),則稱數(shù)列{bn}是數(shù)列{an}的“生成數(shù)列”
(1)若數(shù)列{an}的通項(xiàng)為an=n,寫出數(shù)列{an}的“生成數(shù)列”{bn}的通項(xiàng)公式;
(2)若數(shù)列{cn}的通項(xiàng)為cn=2n+b,(其中b是常數(shù)),試問數(shù)列{cn}的“生成數(shù)列”{ln}是否是等差數(shù)列,請(qǐng)說明理由.
(3)已知數(shù)列{dn}的通項(xiàng)為dn=2n+n,設(shè)數(shù)列{dn}的“生成數(shù)列”{pn}的前n項(xiàng)和為Tn,問是否存在自然數(shù)m滿足滿足(Tm-2012)(Tm-6260)≤0,若存在請(qǐng)求出m的值,否則請(qǐng)說明理由.