| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.95 step avg | 2.82 step avg | 4.58 step avg | 1.97 step avg | 5.69 step avg | 8.63 step avg | 8.43 step avg | 10.25 step avg | 24.83 step avg | 10.43 step avg | 27.31 step avg | 12.15 step avg | 25.20 step avg | 12.08 step avg | 12.10 step avg | 11.49 step avg | 23.52 step avg | 11.60 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 18× | 0s: 1s: 2s: 3s: 4s: 2× 39× 23× 54× 72× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 1× 217× 96× 190× 180× 166× 148× 126× 100× 70× 36× | 0s: 1s: 2s: 3s: 4s: 1× 1,578× 4,476× 1,161× 99× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 1× 2,280× 2,768× 1,801× 3,878× 3,971× 4,572× 5,670× 4,674× 2,517× 1,025× 456× 36× | 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: 1× 3,017× 6,713× 13,594× 25,425× 10,784× 9,818× 11,126× 7,007× 4,893× 3,883× 3,123× 2,886× 2,785× 2,641× 3,613× 852× 728× 2,595× 4,033× 4,893× 3,521× 2,283× 1,449× 1,871× 963× 99× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 1× 10,724× 18,645× 24,541× 28,511× 31,199× 40,080× 53,020× 49,304× 49,011× 39,588× 29,240× 27,487× 21,661× 20,997× 15,785× 7,812× 6,604× 5,188× 1,302× | 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: 1× 4,761× 19,565× 87,193× 109,023× 121,343× 122,505× 137,886× 150,621× 107,562× 97,794× 86,245× 80,605× 57,511× 60,614× 58,909× 51,461× 36,075× 23,000× 20,849× 13,970× 7,182× 13,004× 9,982× 26,572× 14,231× 10,595× 10,495× 5,310× 6,673× 4,349× 3,563× 1,193× 1,218× 351× 64× | 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: 1× 4,958× 14,052× 34,930× 38,988× 52,911× 80,146× 87,344× 136,269× 181,680× 194,112× 163,308× 129,563× 127,798× 144,190× 112,715× 100,245× 105,309× 91,541× 73,493× 56,394× 62,823× 48,639× 51,587× 99,833× 120,313× 116,509× 116,631× 105,428× 87,338× 111,672× 152,184× 220,364× 191,326× 144,518× 115,613× 93,679× 119,199× 145,294× 110,682× 85,656× 61,637× 33,977× 28,428× 45,111× 74,565× 32,606× 14,658× 12,307× 15,592× 14,424× 10,514× 13,059× 13,972× 14,427× 10,940× 9,207× 6,840× 11,219× 13,867× 18,560× 1,680× | 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: 1× 15,754× 88,992× 576,325× 770,490× 912,914× 933,202× 957,216× 968,327× 1,047,334× 868,034× 792,014× 884,161× 839,370× 802,001× 701,609× 561,465× 401,085× 229,882× 158,769× 164,130× 75,061× 95,596× 54,194× 31,977× 35,450× 57,961× 32,875× 26,833× 19,576× 16,268× 2,852× 1,392× | 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: 1× 41,937× 194,903× 405,834× 766,103× 1,112,710× 1,189,396× 1,117,701× 1,156,427× 1,210,462× 865,517× 637,784× 607,503× 543,227× 528,651× 429,425× 311,813× 271,788× 317,148× 528,934× 369,758× 318,976× 346,997× 417,708× 469,133× 560,761× 495,063× 525,986× 630,188× 622,468× 711,082× 903,302× 982,346× 1,117,314× 1,023,808× 788,991× 613,101× 617,130× 660,435× 765,907× 841,999× 1,239,235× 980,789× 746,381× 707,131× 510,844× 421,541× 436,689× 592,701× 829,961× 678,759× 404,547× 379,925× 203,595× 131,573× 108,335× 106,703× 16,028× 11,936× 25,432× 31,036× 12,872× 1,560× | 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: 1× 23,290× 268,892× 2,402,208× 3,696,656× 4,467,475× 5,406,032× 5,119,667× 4,983,672× 5,575,222× 5,678,458× 5,957,297× 5,857,462× 4,947,744× 4,781,233× 4,393,798× 4,701,054× 3,885,064× 2,755,045× 1,964,883× 1,662,974× 1,577,443× 1,556,234× 1,143,898× 736,685× 455,570× 351,342× 382,431× 350,093× 364,333× 219,567× 248,012× 159,172× 106,526× 132,241× 81,950× 64,809× 34,000× 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: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 78s: 1× 125,458× 1,097,772× 2,910,256× 4,471,619× 6,104,686× 8,071,240× 8,594,744× 7,659,119× 6,827,789× 6,933,326× 7,910,729× 7,921,012× 7,254,191× 6,247,345× 6,672,277× 6,117,720× 5,788,897× 5,106,738× 5,159,258× 4,556,441× 4,688,005× 3,814,303× 2,878,476× 2,342,639× 2,116,769× 2,454,599× 2,436,828× 2,211,752× 2,143,488× 1,924,613× 2,644,702× 2,766,607× 2,945,576× 1,719,614× 1,145,183× 1,140,178× 1,118,511× 1,196,388× 863,154× 578,474× 340,934× 302,844× 423,331× 461,412× 313,816× 495,294× 837,652× 1,455,492× 1,758,160× 2,446,905× 1,835,928× 2,247,482× 2,906,022× 2,982,631× 2,737,648× 2,823,886× 2,858,007× 3,578,712× 3,957,599× 2,546,181× 2,347,146× 1,629,174× 1,330,815× 980,747× 740,140× 581,348× 348,536× 429,147× 366,472× 206,387× 451,288× 397,206× 338,164× 91,388× 38,223× 3,913× 2,468× 100× | 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: 1× 25,241× 541,808× 9,324,303× 16,295,356× 18,119,319× 30,932,993× 30,686,025× 30,766,289× 32,301,987× 31,111,410× 35,097,880× 35,766,760× 29,045,385× 25,642,970× 20,658,215× 27,246,372× 25,242,138× 19,982,654× 12,701,638× 8,514,428× 6,122,000× 5,288,410× 4,548,940× 3,256,191× 3,087,704× 2,220,286× 1,591,461× 1,253,042× 1,162,246× 1,081,110× 709,165× 531,741× 380,089× 113,622× 35,024× 26,378× 12,832× 10,241× 1,003× 943× | 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: 1× 664,422× 9,400,600× 30,138,769× 52,488,735× 62,439,385× 79,689,024× 81,652,195× 82,557,122× 75,510,503× 64,157,341× 54,792,328× 50,335,516× 41,209,375× 36,567,332× 31,315,586× 31,765,276× 27,153,426× 26,666,153× 25,344,758× 26,611,328× 22,619,690× 19,884,793× 15,966,028× 13,927,818× 15,954,987× 11,471,392× 9,783,493× 8,610,798× 7,453,996× 5,855,616× 4,849,560× 4,366,531× 3,459,884× 1,531,372× 770,640× 183,627× 5,080× 840× 3,000× | 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: 1× 40,953× 1,441,062× 35,929,122× 65,323,501× 70,709,463× 152,413,614× 169,033,333× 165,259,825× 163,933,383× 155,134,246× 178,720,139× 188,077,146× 162,814,837× 124,313,075× 99,540,298× 107,114,728× 116,175,358× 95,434,268× 53,152,990× 36,370,449× 23,646,368× 13,935,299× 8,956,570× 5,324,903× 3,572,072× 2,803,737× 2,999,994× 1,160,236× 412,929× 101,448× 81,718× 20,520× 5,846× 7,999× | 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: 1× 498,762× 10,768,092× 40,446,213× 71,486,347× 97,219,117× 131,179,026× 151,651,040× 157,771,611× 147,048,488× 141,235,355× 165,475,640× 196,525,458× 194,900,583× 185,535,790× 160,654,257× 153,213,327× 131,333,009× 118,272,790× 96,923,080× 88,055,731× 81,691,582× 95,497,745× 99,261,542× 89,133,453× 67,671,359× 67,880,101× 65,878,505× 60,007,302× 66,150,296× 50,176,169× 58,490,923× 59,534,085× 55,396,068× 51,376,781× 47,439,317× 42,705,141× 34,239,757× 32,176,690× 44,876,487× 48,402,789× 51,281,247× 57,650,379× 58,786,185× 61,410,481× 54,263,158× 54,862,245× 62,538,968× 69,288,977× 57,255,992× 52,381,077× 53,463,150× 51,184,841× 56,397,625× 42,062,951× 31,792,750× 19,004,101× 11,293,081× 8,093,466× 6,051,772× 3,965,035× 6,470,968× 3,539,327× 2,077,500× 2,107,059× 1,410,771× 607,397× 136,980× 8,846× 1,512× | 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: 1× 73,649× 3,676,009× 126,038,269× 242,088,480× 269,709,218× 671,648,095× 812,852,588× 822,460,005× 733,993,854× 628,307,446× 685,490,128× 734,959,458× 691,243,634× 503,815,336× 336,310,818× 360,690,963× 353,834,885× 272,519,491× 143,022,007× 93,297,347× 88,670,871× 88,590,684× 93,291,274× 65,268,676× 46,528,500× 42,369,642× 40,173,402× 27,442,982× 19,593,863× 20,557,398× 17,831,937× 19,522,856× 9,425,851× 6,720,240× 2,444,275× 402,806× 255,728× 12,634× |