We consider the spectrum of the almost Mathieu operator Hα with frequency α
and in the case of the critical coupling. Let an irrational α be such that |α − pn/qn| < cq−κ
n
,
where pn/qn, n = 1, 2, . . . are the convergents to α, and c, κ are positive absolute constants,
κ < 56. Assuming certain conditions on the parity of the coefficients of the continued
fraction of α, we show that the central gaps of Hpn/qn
, n = 1, 2, . . . , are inherited as spectral
gaps of Hα of length at least c
0
q
−κ/2
n , c
0 > 0.