| 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 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.94 step avg | 9.54 step avg | 5.89 step avg | 6.71 step avg | 8.77 step avg | 17.48 step avg | 14.65 step avg | 32.44 step avg | 22.68 step avg | 37.00 step avg | 23.64 step avg | 34.62 step avg | 21.11 step avg | 23.77 step avg | 18.87 step avg | 23.02 step avg | 22.22 step avg | 22.12 step avg | 25.42 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 17× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 0× 1× 17× 0× 0× 0× 0× 0× 0× 5× 76× 72× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 0× 1× 107× 88× 174× 166× 154× 138× 118× 94× 66× 34× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 17× 0× 280× 588× 2,376× 1,067× 881× 441× 334× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 0× 1× 311× 902× 1,308× 2,006× 2,486× 2,502× 2,366× 1,598× 2,708× 4,516× 3,660× 1,664× 306× | 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: 0× 1× 107× 0× 416× 1,365× 3,235× 2,293× 3,913× 4,202× 4,726× 3,937× 5,194× 6,611× 8,753× 6,607× 5,057× 4,289× 3,928× 4,000× 2,228× 1,279× 1,102× 2,106× 861× 2,115× 2,283× 2,997× 3,293× 3,115× 3,011× 2,538× 2,177× 1,210× 236× 828× 652× 282× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 0× 1× 17× 0× 0× 2,630× 4,752× 8,532× 10,978× 12,660× 8,040× 11,070× 16,670× 24,514× 38,200× 52,508× 54,156× 38,996× 22,490× 19,090× 13,008× 5,964× 1,794× 34× | 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: 0× 1× 521× 1,298× 0× 1,526× 4,428× 4,014× 6,713× 15,109× 13,096× 13,001× 14,267× 10,016× 8,521× 8,093× 12,269× 22,285× 28,660× 38,504× 39,829× 32,639× 31,876× 27,652× 27,354× 25,673× 27,498× 17,534× 16,475× 14,804× 17,731× 13,052× 11,434× 14,348× 40,091× 42,224× 33,414× 34,083× 36,446× 36,367× 29,344× 24,400× 33,672× 34,798× 25,708× 27,265× 25,410× 16,729× 15,235× 11,175× 7,611× 10,746× 15,281× 11,453× 5,358× 4,264× 954× 504× 1,404× 2,194× 3,725× 2,930× 3,065× 3,824× 6,443× 1,798× 1,259× 3,058× 3,045× 2,459× 1,010× 786× 540× 250× 816× 216× | 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: 0× 1× 107× 1,750× 4,554× 5,914× 2,502× 372× 0× 0× 0× 0× 0× 16,942× 59,186× 131,010× 195,586× 259,374× 313,500× 283,856× 203,452× 191,872× 136,350× 126,072× 121,100× 148,404× 128,096× 89,430× 84,806× 90,140× 122,458× 112,008× 74,374× 23,938× 14,088× 10,520× 18,468× 20,450× 27,564× 53,442× 34,302× 11,566× 4,842× 2,016× 138× | 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: 0× 1× 1,148× 7,444× 12,066× 17,273× 45,105× 47,729× 48,463× 63,776× 120,767× 143,630× 123,520× 150,493× 159,920× 198,619× 236,709× 249,109× 257,342× 235,127× 210,209× 206,185× 206,168× 160,331× 168,450× 188,153× 248,796× 230,051× 178,507× 130,088× 94,514× 92,770× 73,497× 66,116× 78,194× 78,501× 70,440× 50,413× 39,402× 44,257× 47,904× 58,718× 69,490× 63,344× 60,821× 73,740× 68,537× 81,295× 134,460× 141,801× 154,206× 189,308× 192,379× 231,966× 244,696× 243,587× 206,088× 118,190× 79,666× 70,107× 53,609× 44,758× 50,518× 49,724× 46,753× 66,011× 68,530× 66,678× 60,683× 92,537× 96,077× 91,992× 57,781× 42,315× 51,752× 37,355× 21,480× 22,702× 14,475× 14,709× 19,998× 30,494× 13,761× 10,011× 12,481× 14,276× 8,960× 4,738× 4,494× 2,732× 315× | 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: 0× 1× 3,593× 29,326× 68,854× 75,702× 150,240× 202,876× 174,044× 145,804× 121,010× 127,206× 134,136× 224,692× 331,472× 442,148× 589,464× 905,130× 1,046,506× 1,216,424× 1,388,132× 1,532,138× 1,771,882× 1,586,436× 1,301,032× 1,236,714× 1,183,502× 918,630× 585,814× 338,266× 413,802× 373,578× 283,076× 124,844× 99,094× 117,568× 101,088× 169,932× 239,230× 215,162× 233,694× 251,960× 231,984× 210,554× 135,260× 87,212× 110,282× 68,422× 56,422× 70,112× 35,034× 13,912× 784× | 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: 0× 1× 512× 2,860× 0× 25,832× 370,774× 482,980× 689,421× 730,475× 1,071,615× 1,350,335× 1,301,757× 1,253,194× 1,405,284× 1,369,646× 1,801,217× 2,075,360× 2,347,951× 2,150,678× 2,004,885× 1,780,882× 1,806,372× 1,902,635× 1,904,641× 1,873,043× 1,566,095× 1,363,303× 1,120,966× 962,964× 743,473× 594,137× 442,368× 427,474× 316,636× 260,789× 193,851× 178,359× 90,080× 85,027× 36,380× 63,738× 29,877× 16,670× 5,026× 7,835× 2,440× 3,944× 6,569× 8,838× 292× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 32,784× 388,323× 598,577× 733,478× 981,535× 811,431× 680,183× 593,448× 680,653× 765,699× 971,061× 918,476× 967,509× 697,058× 425,931× 360,301× 317,091× 283,935× 231,265× 236,459× 243,260× 246,892× 141,755× 131,924× 90,458× 224,731× 319,230× 307,837× 151,616× 50,349× 18,696× 3,324× 7,142× 13,589× 15,089× 10,909× 11,786× 2,060× 610× | 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: 0× 1× 521× 5,262× 24,238× 9,976× 0× 26,304× 334,882× 1,012,482× 1,480,852× 3,208,762× 4,323,354× 6,101,552× 7,170,670× 6,697,278× 6,750,340× 5,732,450× 5,981,388× 5,687,008× 5,809,702× 6,244,960× 5,572,770× 5,729,076× 4,805,744× 4,456,746× 4,712,132× 4,709,936× 3,836,252× 3,277,230× 2,869,042× 2,550,220× 2,094,456× 1,965,296× 1,597,158× 1,675,306× 1,377,640× 942,850× 529,618× 285,764× 133,202× 36,634× 642× 154× | 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: 0× 1× 4,766× 41,786× 247,184× 303,400× 2,499,495× 3,418,294× 4,573,004× 5,745,934× 7,281,268× 8,718,764× 8,615,004× 8,662,466× 7,986,582× 7,385,979× 8,309,655× 9,869,238× 12,018,994× 13,767,025× 12,999,388× 12,832,543× 12,460,160× 10,759,212× 9,763,225× 9,868,888× 9,158,457× 7,718,056× 6,479,036× 5,359,428× 4,633,100× 3,265,751× 2,648,201× 2,629,090× 2,670,983× 2,200,019× 1,938,956× 1,779,978× 1,720,598× 1,307,733× 1,012,467× 1,099,515× 921,175× 1,231,297× 1,610,959× 2,088,523× 2,543,452× 2,362,360× 2,770,045× 2,649,060× 2,667,967× 2,891,317× 3,012,076× 1,956,207× 1,626,861× 820,046× 604,093× 507,120× 340,020× 225,839× 153,631× 112,633× 71,111× 104,482× 85,934× 43,869× 20,975× 5,386× 2,464× | 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× 8,177× 159,876× 574,572× 1,475,546× 2,714,088× 3,686,958× 4,736,204× 9,148,122× 11,896,972× 19,470,158× 28,626,574× 32,639,812× 40,294,118× 43,190,280× 45,385,392× 41,218,464× 42,663,442× 38,205,168× 31,869,000× 27,570,438× 20,162,052× 14,641,966× 10,759,212× 9,924,806× 6,970,276× 5,596,380× 5,964,268× 5,950,214× 5,223,806× 5,001,512× 7,298,606× 7,212,438× 6,560,116× 6,547,046× 4,667,876× 4,647,832× 4,253,056× 3,650,634× 2,313,052× 1,236,502× 780,692× 615,354× 186,134× 22,328× 3,200× | 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× 926× 8,698× 115,892× 333,440× 13,685,200× 20,695,235× 22,348,429× 23,963,252× 28,930,052× 36,757,576× 40,310,137× 47,100,984× 40,784,951× 31,566,374× 31,478,301× 38,094,704× 47,223,410× 56,740,458× 61,311,279× 63,475,960× 61,802,875× 54,758,978× 45,802,439× 45,935,224× 43,574,081× 35,636,263× 32,831,697× 28,756,644× 21,108,605× 14,287,118× 10,811,436× 8,745,271× 8,664,881× 7,576,922× 7,230,390× 7,274,075× 5,945,151× 4,570,920× 4,202,179× 4,281,414× 4,148,164× 3,735,737× 3,392,014× 4,609,266× 5,458,449× 5,756,851× 7,403,626× 8,414,681× 7,920,049× 8,571,334× 9,826,672× 7,585,621× 8,068,233× 5,619,104× 5,167,509× 4,331,521× 2,594,959× 2,077,512× 747,915× 277,386× 279,963× 272,539× 222,488× 301,724× 477,675× 548,624× 251,248× 15,309× 5,115× | 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: 0× 1× 13,643× 636,348× 3,876,540× 6,444,916× 9,875,972× 13,122,848× 20,853,858× 23,736,570× 32,275,654× 41,137,160× 45,284,870× 48,565,270× 73,295,080× 85,815,214× 92,444,536× 99,887,326× 100,525,852× 93,266,226× 115,619,150× 132,189,462× 146,849,306× 153,622,980× 145,838,414× 140,590,490× 125,282,662× 101,903,398× 88,764,630× 67,368,544× 57,202,800× 48,140,374× 38,750,264× 28,020,632× 27,410,710× 32,138,716× 28,165,776× 24,057,602× 16,436,232× 9,668,178× 7,611,976× 2,498,020× 635,166× 534,810× 713,832× 1,411,904× 681,496× 401,828× 35,498× 3,486× | 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× 8,702× 623,892× 5,484,252× 3,922,401× 67,247,420× 107,723,310× 97,696,743× 84,983,430× 104,744,688× 125,378,819× 161,660,095× 192,360,005× 190,449,884× 154,118,879× 137,438,062× 152,857,911× 162,675,287× 185,375,821× 214,506,424× 243,787,684× 255,071,096× 233,674,648× 196,597,365× 184,310,469× 158,668,484× 127,180,575× 125,783,097× 121,310,391× 87,595,312× 69,558,011× 58,657,026× 44,468,275× 33,596,790× 24,568,989× 24,664,695× 22,222,618× 20,581,142× 17,021,478× 13,677,561× 15,589,339× 13,911,639× 11,017,187× 8,563,671× 9,581,586× 13,011,298× 16,751,721× 17,551,578× 24,422,945× 24,210,265× 25,241,689× 26,780,742× 23,140,580× 27,652,204× 21,810,234× 14,940,428× 10,541,661× 9,804,466× 5,433,672× 1,805,497× 1,018,352× 590,774× 955,008× 792,972× 121,176× 21,399× 28,553× 25,242× 40× | 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: 0× 1× 521× 6,046× 46,106× 96,096× 5,016,088× 27,684,754× 58,148,424× 123,223,520× 185,124,366× 243,353,304× 280,541,580× 299,328,774× 292,125,448× 260,161,454× 230,623,596× 243,550,948× 232,181,430× 226,712,370× 248,607,366× 291,054,328× 308,978,566× 321,864,594× 279,059,296× 252,615,946× 218,154,044× 245,972,890× 263,848,706× 286,453,676× 268,438,478× 240,843,548× 227,448,740× 226,899,894× 292,139,592× 326,614,322× 302,315,676× 269,779,272× 204,578,024× 165,788,220× 147,511,024× 121,138,076× 116,148,698× 82,603,528× 49,339,260× 35,500,014× 35,112,136× 31,476,858× 19,719,390× 7,360,552× 2,038,178× 157,642× 11,154× 86× |