| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.96 step avg | 4.61 step avg | 7.35 step avg | 12.91 step avg | 10.52 step avg | 19.86 step avg | 19.49 step avg | 37.30 step avg | 47.76 step avg | 52.76 step avg | 53.65 step avg | 46.88 step avg | 101.57 step avg | 43.23 step avg | 79.87 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 22× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 0× 2× 36× 18× 44× 88× 88× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 0× 1× 22× 287× 140× 278× 268× 254× 236× 214× 188× 158× 124× 86× 44× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 0× 1× 22× 0× 0× 0× 0× 0× 0× 0× 0× 0× 3,300× 9,515× 1,969× 143× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 0× 1× 22× 0× 0× 2,272× 4,122× 4,787× 9,388× 11,611× 11,914× 9,772× 6,562× 5,419× 4,489× 5,336× 3,901× 1,134× | 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: 0× 1× 22× 0× 0× 0× 791× 1,639× 2,399× 3,312× 5,603× 7,233× 15,404× 11,746× 15,721× 15,416× 16,734× 33,383× 39,978× 24,464× 21,189× 14,060× 19,018× 19,505× 30,892× 24,928× 11,131× 6,546× 10,449× 8,899× 6,462× 4,691× 3,316× 1,736× 72× | 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: 0× 1× 22× 0× 0× 0× 0× 0× 0× 12,420× 26,907× 53,610× 55,945× 92,320× 110,037× 110,384× 147,256× 171,635× 154,478× 98,220× 85,315× 62,170× 33,330× 21,940× 6,441× 6,164× 13,196× 18,639× 25,135× 31,829× 46,637× 35,991× 19,757× 26,068× 11,298× 21,152× 30,079× 25,319× 6,362× 723× | 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: 0× 1× 22× 0× 0× 0× 791× 2,749× 6,883× 7,803× 1,001× 3,221× 4,736× 1,104× 3,591× 4,764× 1,810× 0× 0× 11,149× 39,968× 160,980× 104,969× 92,330× 170,840× 189,006× 275,623× 290,098× 255,045× 250,257× 203,203× 228,963× 273,499× 221,507× 197,011× 173,400× 109,081× 97,622× 71,160× 50,033× 54,967× 81,451× 70,357× 82,424× 128,449× 154,759× 237,288× 243,885× 158,537× 112,461× 83,449× 105,553× 157,577× 95,883× 128,747× 106,190× 71,948× 68,398× 29,425× 15,554× 11,194× 10,881× 7,475× 30,682× 43,494× 23,888× 21,714× 4,843× 2,300× 3,760× 1,172× | 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: 0× 1× 4,022× 10,888× 30,552× 28,394× 22,821× 11,312× 17,340× 8,711× 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× 146,104× 480,867× 840,082× 1,293,293× 1,664,697× 1,741,304× 1,649,515× 1,469,649× 1,351,297× 1,217,686× 1,145,468× 962,680× 1,071,293× 1,026,714× 958,610× 510,768× 311,933× 380,910× 415,866× 365,573× 247,867× 290,306× 136,575× 110,938× 94,593× 58,338× 52,723× 10,788× 10,560× 5,348× 3,689× | 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: 0× 1× 22× 0× 0× 0× 791× 3,859× 14,688× 8,133× 2,353× 405× 3,322× 0× 0× 0× 0× 0× 0× 0× 0× 29,323× 203,383× 1,265,794× 1,200,841× 1,134,767× 784,294× 543,228× 440,238× 194,936× 156,406× 145,933× 93,533× 158,871× 377,614× 1,218,208× 1,247,068× 1,437,423× 806,711× 533,605× 348,579× 463,363× 519,289× 885,393× 2,957,636× 3,190,521× 3,374,628× 3,769,382× 3,786,713× 3,291,684× 2,837,627× 2,085,019× 1,614,334× 1,835,274× 1,503,164× 1,383,526× 1,112,499× 749,538× 759,997× 627,150× 483,456× 447,735× 437,094× 656,315× 1,004,635× 813,024× 622,787× 665,200× 733,016× 880,576× 691,979× 401,750× 489,865× 495,479× 448,704× 266,672× 146,784× 107,774× 65,503× 68,025× 93,743× 75,395× 25,931× 14,668× 14,680× 44,565× 20,436× 63,308× 72,216× 64,085× 226,668× 124,763× 147,465× 54,658× 18,898× 111,469× 268,389× 527,619× 462,375× 342,515× 221,835× 236,719× 272,218× 188,529× 207,068× 152,358× 68,787× 62,003× 70,437× 43,643× 37,076× 196,453× 240,767× 259,321× 180,557× 114,505× 106,343× 39,990× 10,499× 1,455× 392× | 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: 0× 1× 22× 0× 0× 0× 74,472× 423,061× 920,381× 1,363,816× 1,491,230× 1,321,083× 1,411,305× 1,078,397× 709,773× 868,641× 668,189× 414,521× 460,832× 540,868× 337,393× 324,255× 593,712× 978,228× 1,205,117× 2,177,237× 2,198,248× 2,476,066× 2,305,953× 2,509,166× 2,942,064× 2,199,515× 1,653,548× 1,543,950× 1,015,468× 870,377× 1,049,724× 767,758× 651,999× 225,775× 9,206× 0× 0× 0× 0× 0× 0× 0× 0× 0× 389,319× 1,855,350× 3,752,260× 5,001,880× 6,388,657× 7,407,220× 7,298,934× 7,461,991× 8,644,399× 9,418,137× 11,937,236× 14,021,843× 13,583,720× 12,243,521× 9,378,434× 6,937,844× 5,404,459× 4,450,048× 3,856,951× 2,866,640× 1,947,581× 1,454,295× 1,003,018× 1,211,907× 1,275,846× 946,375× 560,868× 444,627× 492,276× 414,403× 601,078× 543,283× 429,949× 124,383× 6,507× 86× 44× | 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: 0× 1× 5,422× 94,988× 1,376,702× 2,978,866× 2,720,612× 2,329,866× 1,266,544× 809,061× 678,114× 961,945× 866,854× 538,274× 361,103× 1,303,188× 7,056,380× 10,588,337× 10,873,332× 10,607,444× 11,901,995× 15,755,753× 15,297,345× 14,761,069× 14,458,956× 13,103,377× 12,154,005× 10,633,303× 7,693,405× 8,807,684× 8,841,874× 10,859,426× 12,679,025× 15,195,477× 15,551,026× 16,105,972× 16,973,425× 17,776,588× 15,505,895× 13,072,102× 8,898,748× 8,518,075× 7,410,169× 5,323,148× 5,845,001× 5,394,258× 4,742,657× 4,854,455× 2,864,181× 3,108,840× 2,152,759× 2,433,007× 2,910,456× 3,834,458× 3,025,043× 1,848,167× 1,124,963× 1,395,525× 853,306× 823,454× 585,790× 848,928× 1,671,178× 1,577,493× 2,944,818× 1,395,512× 1,081,821× 530,782× 951,334× 899,468× 813,834× 788,759× 1,300,858× 1,969,011× 3,103,269× 4,948,576× 7,712,734× 5,721,655× 5,877,255× 4,335,982× 4,152,660× 6,325,741× 5,233,937× 4,401,628× 3,643,114× 4,267,837× 4,910,327× 4,514,385× 3,567,593× 2,612,731× 1,535,814× 1,276,153× 530,439× 603,937× 389,164× 358,684× 750,377× 1,724,260× 1,551,769× 1,664,461× 2,002,513× 1,056,767× 1,790,145× 2,145,874× 1,105,671× 1,089,312× 1,497,717× 1,301,686× 1,707,337× 2,394,506× 2,664,610× 3,065,436× 3,457,231× 1,824,874× 1,641,844× 1,980,825× 1,414,133× 1,099,146× 1,290,782× 790,420× 1,310,753× 1,095,752× 990,477× 1,091,570× 1,271,738× 1,224,723× 855,772× 751,361× 809,533× 321,910× 152,513× 125,504× 45,604× 6,528× | 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: 136s: 137s: 138s: 139s: 140s: 141s: 142s: 143s: 144s: 145s: 0× 1× 22× 13,720× 70,376× 15,792× 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× 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× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 1,212,492× 10,011,154× 25,510,203× 35,147,843× 48,792,101× 50,965,558× 51,016,476× 57,884,580× 62,011,792× 64,849,631× 63,046,262× 57,788,793× 58,181,970× 62,679,218× 60,989,524× 56,169,342× 49,675,439× 47,356,874× 48,906,393× 41,041,953× 35,861,819× 33,314,594× 37,798,340× 33,703,596× 31,854,390× 33,555,142× 32,270,705× 30,078,182× 25,304,652× 20,232,873× 14,274,776× 9,113,086× 6,814,398× 8,044,194× 9,651,529× 11,420,905× 12,479,178× 14,788,708× 13,109,264× 14,532,488× 15,147,460× 11,665,135× 11,195,955× 10,160,881× 9,565,436× 7,209,767× 5,229,616× 3,618,069× 3,182,228× 2,620,693× 1,964,915× 1,568,326× 2,179,345× 2,175,426× 2,231,109× 1,698,211× 1,240,340× 906,146× 693,866× 417,428× 123,288× 3,832× | 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: 0× 1× 12,022× 96,996× 471,020× 1,820,644× 1,433,619× 1,484,337× 23,282,914× 61,827,249× 64,015,409× 78,740,206× 72,945,693× 54,941,226× 54,356,806× 51,493,077× 69,290,949× 65,819,514× 58,695,812× 45,988,103× 58,212,471× 63,998,619× 55,698,755× 43,083,710× 36,917,886× 33,958,504× 30,921,432× 36,536,555× 34,438,056× 31,228,153× 39,014,333× 45,173,746× 43,998,027× 66,240,989× 73,213,148× 94,715,424× 105,992,001× 116,513,496× 103,001,733× 89,677,870× 70,214,080× 61,107,812× 61,551,875× 47,531,145× 38,052,728× 41,758,260× 38,518,744× 36,183,562× 37,603,364× 41,731,499× 45,596,373× 37,042,359× 47,991,917× 43,904,576× 49,671,587× 49,746,779× 47,958,530× 45,956,290× 47,136,484× 43,465,695× 39,789,121× 34,672,632× 35,387,199× 44,140,484× 45,556,757× 54,844,228× 54,821,632× 56,058,671× 42,676,364× 27,472,934× 31,709,196× 30,655,249× 27,149,788× 20,494,755× 15,700,473× 13,354,230× 10,298,762× 11,302,334× 15,504,781× 21,388,763× 25,140,192× 20,653,045× 22,905,001× 18,327,237× 24,915,849× 26,724,579× 17,948,875× 15,076,900× 14,243,400× 13,116,543× 12,598,168× 10,995,895× 6,433,447× 14,110,687× 14,189,487× 10,499,895× 7,525,879× 7,056,056× 11,341,444× 8,561,395× 5,716,223× 3,463,786× 3,125,452× 2,174,593× 1,475,560× 837,325× 535,296× 719,840× 569,798× 306,483× 51,021× 5,332× | 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× 71,446× 1,037,016× 4,492,012× 6,844,309× 8,752,887× 15,741,474× 17,535,854× 19,097,262× 28,014,898× 34,224,393× 49,284,171× 74,582,275× 66,295,422× 60,635,675× 51,495,623× 39,245,688× 32,518,854× 28,750,924× 18,963,673× 25,523,716× 30,210,254× 42,194,441× 49,910,563× 66,500,252× 60,947,221× 58,490,388× 53,466,435× 61,886,127× 63,738,373× 59,242,169× 62,965,108× 51,148,825× 40,224,415× 51,627,297× 51,614,347× 48,643,423× 50,101,419× 46,970,400× 40,455,647× 45,320,061× 48,491,558× 44,881,482× 36,391,742× 22,978,345× 11,750,020× 7,931,104× 11,305,650× 12,271,744× 8,503,900× 7,878,211× 5,914,707× 2,728,830× 1,431,744× 1,465,708× 695,392× 957,661× 43,904× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 1,811,956× 25,895,765× 75,262,499× 115,811,790× 166,074,267× 220,495,368× 247,282,859× 300,012,408× 304,668,109× 268,831,199× 248,465,843× 236,660,732× 213,067,696× 199,988,131× 190,792,270× 184,395,528× 205,728,102× 228,397,146× 241,967,502× 241,304,209× 246,124,817× 252,758,198× 234,073,652× 176,775,966× 150,559,095× 147,236,396× 170,103,444× 157,850,951× 142,629,200× 136,154,470× 147,296,806× 148,383,277× 164,199,451× 135,131,183× 107,030,181× 90,419,661× 81,289,543× 67,523,983× 63,527,892× 63,911,371× 61,684,604× 67,075,283× 60,213,676× 63,933,282× 47,707,052× 43,630,612× 39,073,860× 31,679,955× 30,543,133× 37,732,104× 30,352,423× 25,631,392× 22,322,636× 23,282,727× 32,323,581× 31,420,594× 22,661,009× 16,724,470× 12,670,293× 6,629,905× 7,620,741× 3,392,525× 1,323,277× 291,270× |