| 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 Full Cycle | 1.95 step avg | 4.57 step avg | 6.56 step avg | 10.95 step avg | 9.00 step avg | 12.60 step avg | 22.43 step avg | 15.21 step avg | 26.82 step avg | 14.40 step avg | 33.32 step avg | 14.79 step avg | 46.16 step avg | 14.64 step avg | 66.62 step avg | 14.27 step avg | 50.88 step avg | 14.38 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 18× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 0× 1× 19× 30× 32× 36× 72× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 0× 1× 18× 199× 96× 190× 180× 166× 148× 126× 100× 70× 36× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 0× 1× 18× 0× 0× 0× 0× 0× 0× 0× 1,560× 4,476× 1,161× 99× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 0× 1× 18× 0× 951× 2,454× 2,117× 2,375× 4,299× 6,246× 6,480× 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: 27s: 28s: 0× 1× 18× 220× 680× 2,318× 5,125× 7,598× 17,516× 19,265× 10,377× 10,432× 9,877× 6,185× 5,334× 4,367× 4,426× 4,805× 2,627× 1,404× 2,875× 4,067× 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: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 28s: 29s: 30s: 31s: 32s: 33s: 0× 1× 18× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 10,706× 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: 36s: 37s: 38s: 39s: 40s: 0× 1× 18× 0× 0× 567× 5,816× 24,126× 87,205× 110,779× 118,962× 122,491× 138,168× 150,601× 108,862× 99,220× 84,184× 75,847× 57,974× 58,768× 58,549× 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: 62s: 63s: 0× 1× 2,018× 8,324× 23,326× 29,204× 45,020× 46,543× 76,410× 84,364× 139,212× 183,577× 193,176× 163,759× 124,228× 126,898× 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: 33s: 34s: 35s: 36s: 37s: 0× 1× 858× 9,292× 88,112× 134,332× 90,800× 209,333× 518,976× 717,110× 1,045,071× 971,709× 1,099,165× 1,189,466× 1,164,366× 1,004,401× 934,417× 896,607× 772,511× 626,822× 423,340× 350,963× 208,747× 159,832× 119,587× 98,164× 40,778× 43,488× 22,625× 12,456× 23,674× 46,311× 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: 63s: 64s: 65s: 66s: 67s: 0× 1× 18× 0× 0× 0× 15,975× 77,439× 160,405× 299,536× 437,734× 486,143× 625,071× 919,943× 1,075,634× 1,109,947× 1,135,693× 1,181,220× 841,667× 607,449× 563,056× 505,473× 527,509× 422,046× 321,589× 282,073× 410,097× 673,057× 566,465× 449,490× 403,372× 412,557× 651,417× 870,857× 823,134× 752,588× 906,626× 993,498× 1,150,163× 1,067,100× 795,103× 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: 39s: 40s: 41s: 0× 1× 1,818× 35,052× 465,756× 927,529× 1,389,810× 2,181,819× 3,236,200× 5,026,157× 5,953,896× 5,981,851× 7,153,454× 7,053,162× 6,553,877× 6,244,007× 5,332,362× 5,628,592× 4,914,850× 4,003,805× 2,996,432× 2,332,057× 1,940,863× 1,605,898× 1,190,598× 862,710× 651,805× 496,026× 390,583× 266,325× 248,688× 200,763× 258,101× 196,876× 221,932× 143,850× 96,692× 127,477× 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: 79s: 80s: 81s: 82s: 83s: 84s: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 0× 1× 18× 0× 11,040× 64,812× 153,140× 86,604× 40,396× 80,000× 3,612× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 114,400× 1,032,960× 2,757,116× 4,385,015× 6,064,290× 7,991,240× 8,591,132× 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: 41s: 42s: 43s: 0× 1× 5,018× 79,068× 1,258,254× 2,938,151× 8,147,351× 14,518,689× 17,630,366× 30,084,581× 32,516,624× 34,708,242× 38,174,013× 36,782,360× 36,420,339× 36,366,133× 29,236,309× 29,165,891× 24,534,479× 23,215,861× 17,802,635× 13,182,056× 9,317,002× 7,440,137× 6,209,404× 5,015,623× 3,616,351× 2,232,365× 2,054,526× 1,894,728× 1,665,935× 1,339,974× 1,182,591× 997,486× 626,854× 500,439× 375,721× 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: 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× 10,386× 142,008× 359,358× 446,256× 202,732× 305,520× 140,192× 76,863× 5,940× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 164,160× 2,524,788× 8,675,620× 15,265,220× 19,905,736× 27,877,499× 25,985,873× 25,500,753× 22,561,532× 14,783,416× 10,645,711× 9,597,083× 6,139,209× 4,793,145× 3,465,121× 3,806,029× 3,767,280× 2,910,800× 1,885,864× 864,628× 466,863× 202,566× 120,420× 3,928× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 489,876× 6,733,804× 21,103,791× 36,777,259× 42,330,917× 51,506,005× 55,526,130× 56,979,506× 52,943,031× 49,373,925× 44,146,617× 40,738,433× 35,070,166× 31,774,187× 27,850,465× 27,959,247× 23,386,146× 23,755,353× 23,458,894× 25,746,700× 22,152,827× 19,682,227× 15,845,608× 13,923,890× 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: 35s: 36s: 37s: 0× 1× 3,162× 140,076× 3,618,608× 8,223,668× 35,310,710× 67,042,146× 74,917,778× 153,106,475× 168,126,267× 162,986,113× 176,527,131× 169,815,989× 185,083,765× 188,860,592× 155,235,432× 129,534,695× 115,797,686× 106,489,462× 92,889,827× 74,395,944× 43,143,464× 29,962,748× 19,622,241× 11,385,762× 9,944,678× 7,072,077× 3,738,981× 1,802,692× 2,435,878× 2,512,542× 3,011,990× 830,603× 232,938× 105,296× 40,146× 13,867× | 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: 0× 1× 18× 16,320× 284,824× 978,620× 1,798,848× 5,066,623× 13,322,992× 19,636,614× 24,424,821× 31,888,762× 31,508,557× 32,703,753× 29,591,158× 25,551,192× 37,925,761× 45,588,759× 49,243,551× 45,116,134× 35,570,493× 39,086,377× 30,909,123× 28,451,714× 22,806,167× 14,489,931× 12,335,011× 16,399,023× 13,864,623× 12,218,212× 5,778,506× 3,186,121× 1,235,755× 8,270,506× 32,278,389× 55,325,737× 74,001,101× 102,924,782× 117,994,864× 120,081,576× 114,315,807× 112,075,733× 128,769,722× 150,582,565× 149,296,695× 139,543,827× 121,894,907× 113,106,375× 98,235,444× 90,206,642× 72,182,765× 73,156,539× 69,268,680× 79,001,875× 85,389,995× 76,915,241× 61,892,853× 64,693,980× 64,993,414× 59,855,212× 66,132,012× 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: 39s: 0× 1× 6,698× 289,756× 9,665,814× 22,437,020× 131,009,375× 268,665,904× 317,310,067× 693,842,161× 783,929,584× 778,850,496× 741,581,079× 647,139,335× 685,522,460× 738,270,351× 681,011,944× 513,965,964× 371,497,036× 367,945,132× 318,811,646× 227,504,901× 130,443,209× 92,933,005× 96,567,983× 99,657,905× 92,734,811× 64,908,274× 50,119,735× 33,080,270× 27,727,808× 25,890,685× 19,245,664× 21,260,468× 10,795,712× 7,343,510× 2,479,384× 416,697× 260,822× 12,634× |