Early in the sequence (i.e., before roundoff error has much effect, if there’s something iterative going on) it seems like a surprising number of our numbers have denominators that are (power of 2) x 10000. As if there’s something happening to 4 decimal places, alongside something happening that involves exact powers of 2. (Cf. Measure’s conjecture that something is keeping track of numerators and denominators separately.) This is all super-handwavy and I don’t have a really concrete hypothesis to offer.
[EDITED to add:] The apparent accumulating roundoff is itself evidence against this, because it means that after a while our numbers are not powers of 2 over 10000. So I’ll be quite surprised if this turns out to be anything other than delusion. I’m leaving it here just in case it gives anyone useful ideas.
Early in the sequence (i.e., before roundoff error has much effect, if there’s something iterative going on) it seems like a surprising number of our numbers have denominators that are (power of 2) x 10000. As if there’s something happening to 4 decimal places, alongside something happening that involves exact powers of 2. (Cf. Measure’s conjecture that something is keeping track of numerators and denominators separately.) This is all super-handwavy and I don’t have a really concrete hypothesis to offer.
[EDITED to add:] The apparent accumulating roundoff is itself evidence against this, because it means that after a while our numbers are not powers of 2 over 10000. So I’ll be quite surprised if this turns out to be anything other than delusion. I’m leaving it here just in case it gives anyone useful ideas.