15830
16105
24297
27606
28086
28118
28393
30441
31134
31190
31465
31958
31977
38889
40406
40569
40681
44502
46550
46701
46825
47574
48342
48361
54891
54998
55017
55766
56041
58838
59113
59799
59862
59881
These numbers are special. Not just in that their Hamming weights are all 10. Well, that’s one part of their specialness.
Guess what? Some of them also turned out to be wrong. At least I think so; I checked by hand, while I used a program (written by myself obviously) to get these numbers. The ones that are definitely in are 59799, 28086, 31134, 27606, 54891, 46701, 40569, 38889. That leaves… 26 left, at least one of which is wrong, and probably most of them. Well, that shows my program is unlikely to have false negatives, just false positives, which aren’t so bad. Maybe. If a parity restriction is added then these 8 confirmed values are the only ones that satisfy the condition.
Hey guess what again? Turns out only those 8 satisfy the condition, parity restriction or not.
