Research Article
On the Probabilistic Proof of the Convergence of the Collatz Conjecture
Table 3
Representative of symmetrical RFs in the table of
even elements.
| | # | F | | F | | F | | F | | F | | F | |
| | 2s | 4 | 16 | 6 | 64 | 8 | 256 | 10 | 1024 | 12 | 4096 | 24 | 16777216 | | 1 | 1 | 22 | 1 | 70 | 1 | 262 | 1 | 1030 | 1 | 4102 | 1 | 16777222 | | 2 | 2 | 28 | 2 | 76 | 2 | 268 | 2 | 1036 | 2 | 4108 | 2 | 16777228 | | 3 | 1 | 34 | 1 | 82 | 1 | 274 | 1 | 1042 | 1 | 4114 | 1 | 16777234 | | 4 | 3 | 40 | 3 | 88 | 3 | 280 | 3 | 1048 | 3 | 4120 | 3 | 16777240 | | 5 | 1 | 46 | 1 | 94 | 1 | 286 | 1 | 1054 | 1 | 4126 | 1 | 16777246 | | 6 | 2 | 52 | 2 | 100 | 2 | 292 | 2 | 1060 | 2 | 4132 | 2 | 16777252 | | 7 | 1 | 58 | 1 | 106 | 1 | 298 | 1 | 1066 | 1 | 4138 | 1 | 16777258 | | 8 | | | 4 | 112 | 4 | 304 | 4 | 1072 | 4 | 4144 | 4 | 16777264 | | 9 | | | 1 | 118 | 1 | 310 | 1 | 1078 | 1 | 4150 | 1 | 16777270 | | 10 | | | 2 | 124 | 2 | 316 | 2 | 1084 | 2 | 4156 | 2 | 16777276 | | 11 | | | 1 | 130 | 1 | 322 | 1 | 1090 | 1 | 4162 | 1 | 16777282 | | 12 | | | 3 | 136 | 3 | 328 | 3 | 1096 | 3 | 4168 | 3 | 16777288 | | 13 | | | 1 | 142 | 1 | 334 | 1 | 1102 | 1 | 4174 | 1 | 16777294 | | 14 | | | 2 | 148 | 2 | 340 | 2 | 1108 | 2 | 4180 | 2 | 16777300 | | 15 | | | 1 | 154 | 1 | 346 | 1 | 1114 | 1 | 4186 | 1 | 16777306 | | 16 | | | 5 | 160 | 5 | 352 | 5 | 1120 | 5 | 4192 | 5 | 16777312 | | 17 | | | 1 | 166 | 1 | 358 | 1 | 1126 | 1 | 4198 | 1 | 16777318 | | 18 | | | 2 | 172 | 2 | 364 | 2 | 1132 | 2 | 4204 | 2 | 16777324 | | 19 | | | 1 | 178 | 1 | 370 | 1 | 1138 | 1 | 4210 | 1 | 16777330 | | 20 | | | 3 | 184 | 3 | 376 | 3 | 1144 | 3 | 4216 | 3 | 16777336 | | 21 | | | 1 | 190 | 1 | 382 | 1 | 1150 | 1 | 4222 | 1 | 16777342 | | 22 | | | 2 | 196 | 2 | 388 | 2 | 1156 | 2 | 4228 | 2 | 16777348 | | 23 | | | 1 | 202 | 1 | 394 | 1 | 1162 | 1 | 4234 | 1 | 16777354 | | 24 | | | 4 | 208 | 4 | 400 | 4 | 1168 | 4 | 4240 | 4 | 16777360 | | 25 | | | 1 | 214 | 1 | 406 | 1 | 1174 | 1 | 4246 | 1 | 16777366 | | 26 | | | 2 | 220 | 2 | 412 | 2 | 1180 | 2 | 4252 | 2 | 16777372 | | 27 | | | 1 | 226 | 1 | 418 | 1 | 1186 | 1 | 4258 | 1 | 16777378 | | 28 | | | 3 | 232 | 3 | 424 | 3 | 1192 | 3 | 4264 | 3 | 16777384 | | 29 | | | 1 | 238 | 1 | 430 | 1 | 1198 | 1 | 4270 | 1 | 16777390 | | 30 | | | 2 | 244 | 2 | 436 | 2 | 1204 | 2 | 4276 | 2 | 16777396 | | 31 | | | 1 | 250 | 1 | 442 | 1 | 1210 | 1 | 4282 | 1 | 16777402 | | 32 | | | | | 6 | 448 | 6 | 1216 | 6 | 4288 | 6 | 16777408 | | 33 | | | | | 1 | 454 | 1 | 1222 | 1 | 4294 | 1 | 16777414 | | 34 | | | | | 2 | 460 | 2 | 1228 | 2 | 4300 | 2 | 16777420 | | 35 | | | | | 1 | 466 | 1 | 1234 | 1 | 4306 | 1 | 16777426 | | 36 | | | | | 3 | 472 | 3 | 1240 | 3 | 4312 | 3 | 16777432 | | 37 | | | | | 1 | 478 | 1 | 1246 | 1 | 4318 | 1 | 16777438 | | 38 | | | | | 2 | 484 | 2 | 1252 | 2 | 4324 | 2 | 16777444 | | 39 | | | | | 1 | 490 | 1 | 1258 | 1 | 4330 | 1 | 16777450 | | 40 | | | | | 4 | 496 | 4 | 1264 | 4 | 4336 | 4 | 16777456 | | 41 | | | | | 1 | 502 | 1 | 1270 | 1 | 4342 | 1 | 16777462 | | 42 | | | | | 2 | 508 | 2 | 1276 | 2 | 4348 | 2 | 16777468 | | 43 | | | | | 1 | 514 | 1 | 1282 | 1 | 4354 | 1 | 16777474 | | 44 | | | | | 3 | 520 | 3 | 1288 | 3 | 4360 | 3 | 16777480 | | 45 | | | | | 1 | 526 | 1 | 1294 | 1 | 4366 | 1 | 16777486 | | 46 | | | | | 2 | 532 | 2 | 1300 | 2 | 4372 | 2 | 16777492 | | 47 | | | | | 1 | 538 | 1 | 1306 | 1 | 4378 | 1 | 16777498 | | 48 | | | | | 5 | 544 | 5 | 1312 | 5 | 4384 | 5 | 16777504 | | 49 | | | | | 1 | 550 | 1 | 1318 | 1 | 4390 | 1 | 16777510 | | 50 | | | | | 2 | 556 | 2 | 1324 | 2 | 4396 | 2 | 16777516 | | 51 | | | | | 1 | 562 | 1 | 1330 | 1 | 4402 | 1 | 16777522 | | 52 | | | | | 3 | 568 | 3 | 1336 | 3 | 4408 | 3 | 16777528 | | 53 | | | | | 1 | 574 | 1 | 1342 | 1 | 4414 | 1 | 16777534 | | 54 | | | | | 2 | 580 | 2 | 1348 | 2 | 4420 | 2 | 16777540 | | 55 | | | | | 1 | 586 | 1 | 1354 | 1 | 4426 | 1 | 16777546 | | 56 | | | | | 4 | 592 | 4 | 1360 | 4 | 4432 | 4 | 16777552 | | 57 | | | | | 1 | 598 | 1 | 1366 | 1 | 4438 | 1 | 16777558 | | 58 | | | | | 2 | 604 | 2 | 1372 | 2 | 4444 | 2 | 16777564 | | 59 | | | | | 1 | 610 | 1 | 1378 | 1 | 4450 | 1 | 16777570 | | 60 | | | | | 3 | 616 | 3 | 1384 | 3 | 4456 | 3 | 16777576 | | 61 | | | | | 1 | 622 | 1 | 1390 | 1 | 4462 | 1 | 16777582 | | 62 | | | | | 2 | 628 | 2 | 1396 | 2 | 4468 | 2 | 16777588 | | 63 | | | | | 1 | 634 | 1 | 1402 | 1 | 4474 | 1 | 16777594 | | 64 | | | | | 7 | 640 | 7 | 1408 | 7 | 4480 | 7 | 16777600 | | 65 | | | | | 1 | 646 | 1 | 1414 | 1 | 4486 | 1 | 16777606 | | 66 | | | | | 2 | 652 | 2 | 1420 | 2 | 4492 | 2 | 16777612 | | 67 | | | | | 1 | 658 | 1 | 1426 | 1 | 4498 | 1 | 16777618 | | 68 | | | | | 3 | 664 | 3 | 1432 | 3 | 4504 | 3 | 16777624 | | 69 | | | | | 1 | 670 | 1 | 1438 | 1 | 4510 | 1 | 16777630 | | 70 | | | | | 2 | 676 | 2 | 1444 | 2 | 4516 | 2 | 16777636 | | 71 | | | | | 1 | 682 | 1 | 1450 | 1 | 4522 | 1 | 16777642 | | 72 | | | | | 4 | 688 | 4 | 1456 | 4 | 4528 | 4 | 16777648 | | 73 | | | | | 1 | 694 | 1 | 1462 | 1 | 4534 | 1 | 16777654 | | 74 | | | | | 2 | 700 | 2 | 1468 | 2 | 4540 | 2 | 16777660 | | 75 | | | | | 1 | 706 | 1 | 1474 | 1 | 4546 | 1 | 16777666 | | 76 | | | | | 3 | 712 | 3 | 1480 | 3 | 4552 | 3 | 16777672 | | 77 | | | | | 1 | 718 | 1 | 1486 | 1 | 4558 | 1 | 16777678 | | 78 | | | | | 2 | 724 | 2 | 1492 | 2 | 4564 | 2 | 16777684 | | 79 | | | | | 1 | 730 | 1 | 1498 | 1 | 4570 | 1 | 16777690 | | 80 | | | | | 5 | 736 | 5 | 1504 | 5 | 4576 | 5 | 16777696 | | 81 | | | | | 1 | 742 | 1 | 1510 | 1 | 4582 | 1 | 16777702 | | 82 | | | | | 2 | 748 | 2 | 1516 | 2 | 4588 | 2 | 16777708 | | 83 | | | | | 1 | 754 | 1 | 1522 | 1 | 4594 | 1 | 16777714 | | 84 | | | | | 3 | 760 | 3 | 1528 | 3 | 4600 | 3 | 16777720 | | 85 | | | | | 1 | 766 | 1 | 1534 | 1 | 4606 | 1 | 16777726 | | 86 | | | | | 2 | 772 | 2 | 1540 | 2 | 4612 | 2 | 16777732 | | 87 | | | | | 1 | 778 | 1 | 1546 | 1 | 4618 | 1 | 16777738 | | 88 | | | | | 4 | 784 | 4 | 1552 | 4 | 4624 | 4 | 16777744 | | 89 | | | | | 1 | 790 | 1 | 1558 | 1 | 4630 | 1 | 16777750 | | 90 | | | | | 2 | 796 | 2 | 1564 | 2 | 4636 | 2 | 16777756 | | 91 | | | | | 1 | 802 | 1 | 1570 | 1 | 4642 | 1 | 16777762 | | 92 | | | | | 3 | 808 | 3 | 1576 | 3 | 4648 | 3 | 16777768 | | 93 | | | | | 1 | 814 | 1 | 1582 | 1 | 4654 | 1 | 16777774 | | 94 | | | | | 2 | 820 | 2 | 1588 | 2 | 4660 | 2 | 16777780 | | 95 | | | | | 1 | 826 | 1 | 1594 | 1 | 4666 | 1 | 16777786 | | 96 | | | | | 6 | 832 | 6 | 1600 | 6 | 4672 | 6 | 16777792 | | 97 | | | | | 1 | 838 | 1 | 1606 | 1 | 4678 | 1 | 16777798 | | 98 | | | | | 2 | 844 | 2 | 1612 | 2 | 4684 | 2 | 16777804 | | 99 | | | | | 1 | 850 | 1 | 1618 | 1 | 4690 | 1 | 16777810 | | 100 | | | | | 3 | 856 | 3 | 1624 | 3 | 4696 | 3 | 16777816 | | 101 | | | | | 1 | 862 | 1 | 1630 | 1 | 4702 | 1 | 16777822 | | 102 | | | | | 2 | 868 | 2 | 1636 | 2 | 4708 | 2 | 16777828 | | 103 | | | | | 1 | 874 | 1 | 1642 | 1 | 4714 | 1 | 16777834 | | 104 | | | | | 4 | 880 | 4 | 1648 | 4 | 4720 | 4 | 16777840 | | 105 | | | | | 1 | 886 | 1 | 1654 | 1 | 4726 | 1 | 16777846 | | 106 | | | | | 2 | 892 | 2 | 1660 | 2 | 4732 | 2 | 16777852 | | 107 | | | | | 1 | 898 | 1 | 1666 | 1 | 4738 | 1 | 16777858 | | 108 | | | | | 3 | 904 | 3 | 1672 | 3 | 4744 | 3 | 16777864 | | 109 | | | | | 1 | 910 | 1 | 1678 | 1 | 4750 | 1 | 16777870 | | 110 | | | | | 2 | 916 | 2 | 1684 | 2 | 4756 | 2 | 16777876 | | 111 | | | | | 1 | 922 | 1 | 1690 | 1 | 4762 | 1 | 16777882 | | 112 | | | | | 5 | 928 | 5 | 1696 | 5 | 4768 | 5 | 16777888 | | 113 | | | | | 1 | 934 | 1 | 1702 | 1 | 4774 | 1 | 16777894 | | 114 | | | | | 2 | 940 | 2 | 1708 | 2 | 4780 | 2 | 16777900 | | 115 | | | | | 1 | 946 | 1 | 1714 | 1 | 4786 | 1 | 16777906 | | 116 | | | | | 3 | 952 | 3 | 1720 | 3 | 4792 | 3 | 16777912 | | 117 | | | | | 1 | 958 | 1 | 1726 | 1 | 4798 | 1 | 16777918 | | 118 | | | | | 2 | 964 | 2 | 1732 | 2 | 4804 | 2 | 16777924 | | 119 | | | | | 1 | 970 | 1 | 1738 | 1 | 4810 | 1 | 16777930 | | 120 | | | | | 4 | 976 | 4 | 1744 | 4 | 4816 | 4 | 16777936 | | 121 | | | | | 1 | 982 | 1 | 1750 | 1 | 4822 | 1 | 16777942 | | 122 | | | | | 2 | 988 | 2 | 1756 | 2 | 4828 | 2 | 16777948 | | 123 | | | | | 1 | 994 | 1 | 1762 | 1 | 4834 | 1 | 16777954 | | 124 | | | | | 3 | 1000 | 3 | 1768 | 3 | 4840 | 3 | 16777960 | | 125 | | | | | 1 | 1006 | 1 | 1774 | 1 | 4846 | 1 | 16777966 | | 126 | | | | | 2 | 1012 | 2 | 1780 | 2 | 4852 | 2 | 16777972 | | 127 | | | | | 1 | 1018 | 1 | 1786 | 1 | 4858 | 1 | 16777978 | | 128 | | | | | | | 8 | 1792 | 8 | 4864 | 8 | 16777984 | | | | | | | | | … | … | … | … | … | … |
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