| Radix Character Encoding | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V |
| Color Key | ||
|---|---|---|
| Orange | Fixed Point | number that becomes itself after one iteration |
| Green | Final Numbers | all numbers eventually reached, from all cycles |
| Purple | Cycle Start | iterations include entry into cycle, assuming it repeats |
| Red | Full Cycle | iterations include entire cycle, proving it repeats |
| Blue | Start Numbers | subset (optimization) of all numbers; minimal for full coverage |
| Gray | No Results | any calculation that has no results |
| Digits | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.95 step avg | 6.55 step avg | 6.96 step avg | 7.36 step avg | 9.58 step avg | 28.68 step avg | 13.05 step avg | 22.89 step avg | 25.54 step avg | 70.04 step avg | 66.19 step avg | 33.06 step avg | 44.94 step avg | 45.29 step avg | 78.16 step avg | 44.57 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 20× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 20× 10× 0× 3× 52× 45× 100× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 0× 1× 20× 241× 117× 232× 222× 208× 190× 168× 142× 112× 78× 40× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 20× 0× 526× 1,203× 285× 1,784× 5,562× 1,125× 120× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 468× 949× 1,306× 2,529× 3,541× 5,452× 5,231× 4,374× 6,559× 6,929× 6,565× 4,947× 2,900× 1,021× 358× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 0× 1× 20× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 2,334× 6,297× 9,098× 3,587× 4,073× 6,585× 7,506× 9,072× 11,126× 10,090× 5,582× 6,500× 7,303× 7,563× 7,264× 9,155× 11,086× 10,579× 14,865× 13,126× 10,525× 11,194× 7,694× 8,621× 5,737× 9,203× 4,735× 3,457× 1,555× 2,242× 1,322× 629× 504× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 0× 1× 20× 4,700× 7,060× 21,337× 40,852× 55,165× 74,095× 89,401× 83,107× 61,852× 49,418× 32,392× 21,165× 29,630× 29,145× 32,057× 58,774× 65,104× 48,553× 37,695× 24,411× 7,614× 5,882× 5,237× 1,830× 1,533× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 0× 1× 804× 2,200× 1,589× 3,624× 16,318× 18,145× 48,199× 141,138× 129,830× 139,303× 105,052× 84,125× 60,326× 48,220× 60,993× 47,061× 36,062× 45,378× 100,148× 112,273× 153,124× 176,409× 176,651× 155,198× 149,361× 150,340× 165,756× 120,506× 57,768× 92,785× 75,544× 62,262× 42,822× 22,887× 42,439× 55,559× 65,279× 57,129× 19,753× 21,300× 17,799× 14,439× 11,955× 251× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 0× 1× 3,020× 18,368× 47,892× 52,599× 44,297× 47,560× 103,885× 189,969× 293,065× 353,606× 452,765× 387,694× 394,668× 294,319× 195,479× 96,265× 114,500× 203,186× 323,368× 418,163× 381,750× 397,787× 304,917× 406,943× 324,233× 324,975× 211,322× 181,911× 177,030× 214,360× 221,417× 211,918× 210,681× 154,331× 137,055× 133,899× 195,236× 211,195× 206,227× 169,787× 116,073× 118,526× 74,551× 69,679× 110,416× 148,619× 222,160× 198,148× 108,248× 28,339× 6,231× 1,292× 860× 220× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 104s: 105s: 106s: 107s: 108s: 109s: 110s: 0× 1× 468× 784× 681× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 37,873× 222,746× 750,451× 987,980× 470,214× 306,987× 270,930× 160,199× 237,768× 136,114× 190,180× 150,398× 239,510× 364,898× 695,786× 980,306× 1,239,452× 656,704× 713,467× 1,036,626× 786,543× 835,555× 765,058× 769,482× 435,958× 386,428× 502,660× 505,495× 406,603× 274,254× 195,745× 263,049× 150,508× 199,277× 171,848× 388,238× 350,796× 458,039× 250,824× 185,954× 221,227× 259,296× 524,579× 794,424× 636,499× 426,324× 485,328× 514,804× 222,003× 168,717× 244,467× 339,609× 593,017× 605,990× 544,536× 663,285× 715,396× 818,242× 772,136× 455,690× 359,732× 431,088× 262,763× 263,642× 176,554× 160,111× 113,812× 43,295× 62,491× 21,501× 4,558× 5,110× 1,952× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 0× 1× 804× 1,344× 0× 0× 23,560× 80,213× 127,410× 181,528× 181,707× 206,178× 301,608× 509,140× 633,452× 999,779× 1,236,727× 1,192,431× 892,443× 499,874× 244,327× 191,671× 192,426× 161,300× 35,944× 6,741× 4,420× 2,716× 1,224× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 295,562× 1,365,703× 2,742,879× 3,361,098× 3,878,234× 4,504,290× 4,181,080× 4,241,682× 4,688,244× 4,957,452× 4,624,489× 4,544,889× 4,611,440× 4,778,199× 3,900,049× 2,995,607× 2,150,446× 1,401,385× 1,267,406× 1,488,062× 1,466,868× 1,473,827× 1,161,917× 1,032,328× 1,000,255× 1,157,357× 1,015,454× 847,499× 642,180× 485,382× 299,436× 105,864× 66,269× 25,537× 4,186× 792× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 0× 1× 20× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 31,886× 341,585× 1,715,309× 6,635,183× 7,448,757× 12,572,409× 11,701,435× 10,256,638× 10,859,797× 7,784,882× 7,965,646× 10,625,923× 11,824,231× 14,606,720× 18,302,792× 14,695,824× 14,042,468× 13,214,223× 10,580,899× 7,717,725× 8,108,586× 7,550,167× 5,113,509× 2,407,406× 1,725,911× 2,478,900× 1,860,827× 1,956,291× 798,313× 239,513× 466,069× 144,437× 6,878× 7,414× 2,164× 1,060× 808× 234× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 0× 1× 13,092× 198,152× 678,904× 852,410× 354,781× 397,689× 922,179× 2,204,197× 4,046,109× 6,453,111× 7,478,231× 9,473,408× 11,210,560× 11,741,449× 12,199,267× 13,308,722× 13,585,066× 13,039,395× 11,306,538× 9,883,538× 9,770,851× 11,039,634× 13,125,266× 13,377,269× 11,208,867× 8,972,140× 8,323,152× 10,205,696× 11,024,056× 9,783,542× 7,293,626× 5,435,879× 3,247,627× 2,378,970× 2,603,042× 2,141,202× 1,903,579× 2,143,048× 2,936,124× 2,436,321× 2,712,183× 3,072,570× 4,143,365× 6,168,896× 8,698,164× 8,207,444× 8,090,429× 7,521,682× 7,729,145× 7,441,633× 8,491,607× 8,793,989× 10,062,698× 11,064,757× 8,346,476× 6,464,307× 7,930,452× 8,825,652× 8,699,157× 5,462,204× 4,906,147× 4,933,358× 5,853,004× 7,588,765× 7,228,463× 6,123,258× 5,488,130× 5,065,801× 5,658,419× 5,400,169× 3,956,951× 3,805,458× 3,869,293× 3,690,068× 5,037,277× 4,316,549× 4,795,758× 5,121,598× 5,514,148× 5,822,869× 4,763,772× 5,739,796× 6,839,180× 5,058,835× 3,438,069× 3,622,555× 3,913,754× 3,669,370× 2,338,552× 1,704,969× 1,127,016× 1,521,320× 2,616,046× 1,290,164× 1,039,603× 1,017,865× 1,020,802× 607,321× 491,167× 399,736× 104,557× 43,008× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 0× 1× 8,004× 74,032× 103,180× 11,568× 4,353× 0× 45,229× 800,922× 3,587,595× 16,435,810× 9,275,681× 7,501,815× 8,292,166× 13,035,951× 14,794,251× 10,873,580× 10,935,973× 19,273,853× 14,353,422× 8,781,249× 7,022,653× 8,296,669× 10,411,880× 8,953,112× 3,045,064× 2,131,966× 2,442,209× 12,675,589× 48,519,338× 60,425,470× 68,774,546× 70,076,358× 58,510,831× 54,926,875× 56,542,717× 51,014,470× 55,604,215× 53,726,317× 43,825,605× 27,767,837× 18,145,077× 18,823,573× 19,107,348× 27,524,494× 23,949,002× 13,578,678× 10,564,010× 9,784,739× 11,051,613× 13,340,990× 9,543,836× 8,513,172× 5,710,217× 5,153,438× 5,742,507× 5,046,533× 2,097,307× 1,543,071× 1,694,731× 3,755,504× 6,631,646× 3,657,462× 4,934,808× 10,392,543× 9,238,141× 12,608,253× 10,658,772× 9,751,440× 12,073,929× 10,314,010× 9,494,064× 7,029,594× 10,062,417× 6,034,887× 1,819,221× 2,488,461× 8,125,807× 18,007,294× 22,475,178× 16,468,413× 17,343,503× 17,672,564× 12,995,321× 8,289,511× 7,002,339× 11,043,216× 23,289,858× 13,126,728× 6,157,421× 6,080,070× 3,756,376× 2,698,715× 1,104,054× 1,740,131× 3,315,282× 3,120,566× 1,756,457× 1,001,528× 387,530× 201,853× 64,709× 9,372× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 104s: 105s: 106s: 107s: 108s: 109s: 110s: 111s: 112s: 113s: 114s: 115s: 116s: 117s: 118s: 119s: 120s: 121s: 122s: 123s: 124s: 125s: 126s: 127s: 128s: 129s: 130s: 131s: 132s: 133s: 134s: 135s: 0× 1× 468× 1,568× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 378,480× 4,749,876× 14,632,199× 26,078,501× 32,858,713× 39,728,442× 39,201,348× 45,018,005× 48,346,996× 40,785,955× 27,600,264× 21,184,215× 23,226,748× 17,829,849× 12,262,124× 10,425,857× 11,379,995× 12,792,510× 20,436,327× 18,606,886× 17,228,835× 15,736,291× 11,697,080× 5,235,900× 3,534,366× 3,626,667× 3,295,327× 4,016,287× 9,920,028× 17,918,843× 20,260,697× 17,813,677× 20,977,855× 23,206,993× 25,886,521× 30,814,120× 34,767,156× 48,505,388× 61,425,326× 70,301,277× 71,602,913× 77,859,774× 71,417,223× 76,497,955× 60,661,997× 52,199,882× 47,308,627× 43,392,643× 49,494,431× 62,099,817× 77,301,643× 75,842,912× 86,323,422× 69,166,584× 56,102,062× 53,176,029× 59,261,645× 59,974,508× 51,300,453× 48,209,428× 44,922,570× 48,133,156× 47,223,535× 49,867,737× 44,378,186× 36,903,900× 35,335,941× 37,270,022× 42,567,581× 46,802,101× 47,706,192× 56,616,389× 47,559,274× 44,400,167× 40,685,992× 34,252,483× 30,522,753× 30,055,015× 34,271,320× 34,284,669× 32,826,401× 27,468,610× 24,749,557× 19,557,271× 17,808,102× 15,331,812× 12,344,554× 13,708,171× 10,638,685× 10,689,984× 9,041,398× 7,123,460× 9,056,234× 10,399,413× 9,971,157× 5,213,121× 4,798,951× 2,170,231× 2,180,696× 2,149,119× 1,212,645× 846,516× 898,526× 656,733× 269,787× 138,126× 47,008× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 34s: 35s: 36s: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 0× 1× 804× 2,016× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 84,970× 1,623,405× 10,896,697× 50,034,043× 98,334,872× 91,574,964× 72,689,638× 96,336,398× 95,683,739× 76,055,570× 78,751,948× 136,781,492× 171,876,958× 152,338,369× 131,972,281× 130,545,527× 277,750,776× 350,835,806× 314,307,932× 261,055,586× 207,682,227× 213,471,818× 188,847,323× 136,351,820× 158,905,079× 181,283,392× 124,543,685× 90,131,602× 103,199,647× 109,133,001× 111,079,531× 79,183,404× 59,961,852× 40,193,700× 25,293,418× 52,580,214× 76,920,169× 53,107,290× 72,193,706× 93,705,212× 86,167,144× 81,738,574× 73,467,325× 88,220,206× 95,198,895× 121,976,248× 175,208,007× 143,348,205× 150,183,102× 139,776,638× 108,927,521× 87,656,903× 120,769,149× 125,816,937× 92,389,794× 103,259,075× 84,252,585× 102,701,835× 117,863,171× 110,995,526× 79,921,367× 53,519,821× 37,507,925× 29,952,326× 34,444,783× 36,847,742× 31,774,111× 11,023,318× 2,516,435× 1,328,537× 870,227× 858,410× 77,836× 5,100× 5,450× |