Post B2xWjwfA4bbLUo7qU4 by pr1ncess@social.xenofem.me
 (DIR) More posts by pr1ncess@social.xenofem.me
 (DIR) Post #B2xBHCfROMCfhJi4DQ by erin@social.xenofem.me
       2026-02-03T19:11:30.667037Z
       
       2 likes, 0 repeats
       
       (1) 2, 4, 8, 16, 32, 64, 128…(2) 2, 2…(3) 2, 4, 4…(4) 2, 4, 2…(5) 2, 4, 8, 8…(6) 2, 4, 8, 6, 3, 9, 12, 6…(7) 2, 4, 8, 4…(8) 2, 4, 8, 2…(9) 2, 4, 8, 16, 16…(10) 2, 4, 8, 16, 14, 35, 56, 77, 154, 110, 22, 44, 88, 176, 154…(11) 2, 4, 8, 16, 12, 6, 18, 24, 12…(12) 2, 4, 8, 16, 10, 50, 30, 40, 35, 91, 182, 78, 156, 26, 52, 104, 208, 130, 260, 234, 182…(13) 2, 4, 8, 16, 8…(14) 2, 4, 8, 16, 6, 18, 15, 10, 50, 55, 176, 220, 132, 165, 242, 88, 110, 209, 266, 114, 190, 399, 171, 285, 228, 133, 380, 304, 342, 323, 209…(15) 2, 4, 8, 16, 4…(16) 2, 4, 8, 16, 2…
       
 (DIR) Post #B2xUuUTb0is1M0cHtQ by erin@social.xenofem.me
       2026-02-03T22:51:33.187335Z
       
       0 likes, 0 repeats
       
       I double-checked these with a computer but shockingly there were no mistakes in the original post (assuming my program is correct). I guess I was just locked in. Here are a couple others:(90) 2, 4, 8, 16, 32, 64, 128, 78, 1014, 455, 130, 533, 3608, 1968, 4059, 2214, 3198, 3403, 9130, 4316, 11039, 7636, 13280, 8964, 5312, 5063, 6557, 12367, 12665, 17284, 2682, 15049, 14453, 18476, 7897, 22946, 24138, 16092, 23989, 20413, 18029, 7599, 18327, 12218, 16986, 11324, 16390, 2086, 5811, 17135, 7003, 22350, 14900, 18774, 12516, 8344, 9983, 15496, 14751, 23095, 19817, 8791, 10281, 6854, 13410, 8940, 5960, 12814, 12963, 8642, 1341, 14155, 13857, 22499, 24160, 19630, 7550, 24613, 7987, 25265, 12714, 12388, 17278, 16463, 14181, 19397, 13692, 12225, 19723, 8802, 13040, 22005, 18093, 4238, 8965, 10595, 15159, 19234, 16137, 19071, 18582, 11410, 17441, 14018, 21842, 20538, 11084, 7824, 27710, 19560, 11247, 19886, 20864, 20701, 8639, 15485, 14344, 16952, 6846, 13366, 17115, 4401, 21027, 18256, 16300, 2119, 11736, 12551, 14833, 24124, 15322, 16789, 9291, 5705, 15974, 21516, 10921, 10269, 5542, 18419, 13855, 24287, 27384, 9943, 10432, 17604, 11573, 14996, 21679, 22983, 17930, 6683, 15811, 23961, 17767, 9128, 8150, 8313, 5868, 13529, 14670, 12062, 7661, 15648, 26406, 10106, 7987...(ω) 2, 4, 2, 4, 2, 4, 8, 4, 8, 16, 14, 28, 42, 42, 21, 49, 28, 84, 112, 154, 231, 121, 176, 242, 132, 132, 77, 275, 352, 176, 341, 341, 961, 1023, 1023, 1147, 2294, 962, 1369, 1443, 1443, 1591, 3182, 1376, 1849, 1935, 1935, 2107, 3698, 2150 [this one can easily be shown to never converge into a cycle]The "twins" in the omega one are super cool, I'm wondering if there's any regularity to them and if there's infinitely many of them. Gonna look into that
       
 (DIR) Post #B2xWjwfA4bbLUo7qU4 by pr1ncess@social.xenofem.me
       2026-02-03T22:58:46.070780Z
       
       1 likes, 0 repeats
       
       @erin what series is this?
       
 (DIR) Post #B2xYK792g9hKNsue0W by erin@social.xenofem.me
       2026-02-03T23:29:39.965123Z
       
       0 likes, 0 repeats
       
       @pr1ncess I made it up myself, though it might already have existed. Can you figure out how it was constructed?It's recommended to look at the first post with the smaller sequences, as they're easier to study. In particular, you might get something out of looking at (10) in isolation.Anyway, I used my program to compute the indices of every twin up to index 100,000 in the omega sequence. Here's a list of those indices:13, 25, 31, 34, 40, 46, 142, 196, 202, 589, 697, 1001, 1173, 1209, 1385, 1926, 2289, 2343, 2689, 2782, 2787, 5001, 7480, 9081, 9595, 15196, 17330, 18753, 19621, 21563, 24085, 31389, 35379, 42101, 45271, 53817, 71521, 92977, 95130, 98449They seem to get much sparser over time, which makes sense to me, but from a logarithmic perspective it's strange for sure. We have 6 twins with two-digit indices, 5 with three-digit indices, then 14 with four-digit indices and 15 with five-digit indices.I also tried starting with different initial values other than 2, and I noticed that the same indices recurred again and again. For instance, 1173 is a twin index for starting values 2, 3, 4, 5, 39, 69, and 1001 (though not 101 or 1002), and likely many more as those are the only ones I've tested so far. I really wonder what that's all about.