It is known that the sum of the first n terms of the sequence {an} is Sn and satisfies Sn = 2an-n, (n ∈ n *) (1) find the general term formula of the sequence {an}; (2) if BN = (2n + 1) an + 2n + 1 and the sum of the first n terms of the sequence {BN} is TN, find the minimum n value satisfying the inequality tn-22n-1 ≥ 128

It is known that the sum of the first n terms of the sequence {an} is Sn and satisfies Sn = 2an-n, (n ∈ n *) (1) find the general term formula of the sequence {an}; (2) if BN = (2n + 1) an + 2n + 1 and the sum of the first n terms of the sequence {BN} is TN, find the minimum n value satisfying the inequality tn-22n-1 ≥ 128

(1) Because Sn = 2an-n, so sn-1 = 2an-1 - (n-1), (n ≥ 2, n ∈ n *), subtracting the two formulas to obtain an = 2an-1 + 1, so an + 1 = 2 (an-1 + 1), (n ≥ 2, n ∈ n *), and because a1 + 1 = 2, so {an + 1} is an equal ratio sequence with the first term of 2 and the common ratio of 2, so an + 1 = 2n, so an = 2N-1