| 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 |
| W | X | Y | Z | a | b | c | d | e | f | g | h | i | j | k | l |
| 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 |
|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.98 step avg | 7.53 step avg | 11.17 step avg | 8.84 step avg | 12.98 step avg | 30.34 step avg | 22.52 step avg | 38.94 step avg | 21.97 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 42× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 42× 21× 42× 3× 112× 95× 210× 420× | 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: 0× 1× 42× 967× 480× 958× 948× 934× 916× 894× 868× 838× 804× 766× 724× 678× 628× 574× 516× 454× 388× 318× 244× 166× 84× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 0× 1× 42× 0× 0× 0× 0× 0× 38,500× 112,630× 11,529× 483× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 0× 1× 42× 0× 9,951× 26,454× 25,023× 33,032× 64,080× 76,600× 119,358× 141,070× 179,330× 163,259× 188,172× 128,326× 143,230× 89,526× 68,616× 44,107× 23,164× 9,067× 1,531× | 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× 42× 0× 0× 0× 0× 0× 0× 12,620× 30,246× 104,853× 466,280× 195,739× 128,646× 98,573× 105,556× 138,881× 151,389× 151,385× 232,060× 337,649× 330,952× 511,577× 485,865× 565,910× 491,569× 636,464× 414,257× 374,935× 483,111× 361,268× 305,046× 349,432× 500,425× 496,448× 487,846× 476,124× 464,877× 463,057× 318,067× 232,498× 202,968× 140,295× 141,404× 114,773× 89,678× 81,369× 70,846× 70,788× 71,669× 51,498× 51,403× 43,462× 22,293× 27,870× 15,811× 23,916× 26,367× 10,941× 10,388× 12,673× 13,593× 17,225× 13,559× 16,549× 7,347× 16,538× 1,599× 844× 198× | 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× 42× 0× 0× 0× 0× 0× 0× 134,080× 349,900× 744,727× 1,154,706× 1,905,382× 2,570,929× 3,376,109× 4,462,275× 4,908,984× 5,310,647× 6,251,151× 6,930,629× 8,133,875× 7,189,885× 5,485,299× 3,836,518× 2,709,657× 1,854,837× 1,378,321× 1,126,669× 964,034× 999,493× 922,341× 1,329,787× 1,834,012× 1,793,761× 1,939,228× 1,683,128× 1,483,771× 1,302,520× 813,392× 505,592× 303,401× 173,553× 37,737× 211× | 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: 0× 1× 42× 16,616× 96,931× 511,249× 1,222,277× 1,638,054× 2,506,706× 3,308,355× 4,627,559× 6,682,806× 8,334,666× 8,758,722× 7,004,232× 6,785,710× 8,999,663× 8,409,365× 7,492,559× 8,532,379× 9,382,947× 10,696,768× 10,809,779× 10,626,330× 10,579,147× 10,854,239× 13,281,595× 12,889,880× 11,006,362× 12,347,557× 11,458,641× 12,289,139× 11,248,067× 12,234,180× 12,541,511× 12,468,929× 12,371,831× 12,071,973× 11,669,370× 10,623,704× 10,045,276× 8,955,442× 10,405,438× 10,714,442× 9,443,705× 7,881,120× 8,666,855× 8,026,455× 7,431,722× 6,956,789× 6,553,270× 6,372,856× 5,525,431× 7,318,222× 6,047,655× 5,028,390× 3,834,093× 3,609,627× 4,080,282× 3,495,403× 3,328,716× 2,278,561× 2,551,101× 2,450,500× 2,600,852× 2,650,698× 1,673,339× 1,408,906× 1,821,968× 2,801,087× 3,682,294× 2,961,128× 2,516,759× 2,571,718× 3,862,654× 3,112,180× 3,144,995× 2,258,764× 2,230,827× 1,766,749× 1,695,532× 2,526,486× 2,107,535× 1,603,218× 1,750,788× 1,815,965× 2,468,959× 1,394,695× 1,413,296× 1,814,653× 1,350,292× 1,288,998× 722,499× 256,298× 395,403× 250,999× 274,868× 175,807× 98,664× 89,432× 143,054× 589,411× 563,543× 960,491× 623,735× 531,894× 304,987× 327,969× 273,236× 432,851× 106,603× 37,046× 14,021× 12,128× 15,622× 1,562× | 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: 0× 1× 70,026× 586,888× 2,164,634× 5,157,105× 11,382,945× 20,614,090× 37,880,806× 53,170,096× 65,754,311× 77,713,443× 99,391,828× 102,801,621× 108,213,780× 118,284,724× 111,079,662× 127,510,122× 127,164,348× 145,107,265× 153,690,614× 169,257,354× 179,012,670× 162,928,174× 149,616,918× 115,515,135× 99,490,257× 103,312,061× 92,410,335× 81,823,875× 66,262,390× 51,701,207× 43,505,656× 39,997,882× 42,932,526× 49,865,541× 48,879,292× 30,568,387× 33,853,293× 27,565,352× 21,583,223× 21,317,948× 18,180,865× 14,530,473× 7,571,285× 2,001,611× 336,567× 176,976× 376,788× |