| 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 Cycle Start | 0.98 step avg | 4.62 step avg | 9.93 step avg | 1.83 step avg | 10.54 step avg | 27.10 step avg | 14.82 step avg | 38.07 step avg | 22.68 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 46× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 2× 76× 38× 92× 184× 368× 368× | 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: 1× 1,197× 572× 1,142× 1,132× 1,118× 1,100× 1,078× 1,052× 1,022× 988× 950× 908× 862× 812× 758× 700× 638× 572× 502× 428× 350× 268× 182× 92× | 0s: 1s: 2s: 3s: 4s: 1× 54,694× 160,149× 14,881× 575× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 1× 17,390× 24,186× 28,436× 65,420× 88,276× 140,582× 175,533× 216,162× 206,466× 262,161× 199,794× 204,880× 178,851× 148,105× 127,546× 88,274× 59,035× 41,444× 40,591× 26,793× 9,134× | 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: 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: 1× 75,211× 153,834× 286,023× 357,248× 438,875× 554,610× 273,635× 305,038× 229,014× 231,328× 179,751× 182,439× 138,557× 343,253× 662,716× 469,707× 242,370× 439,505× 696,752× 1,036,372× 680,158× 559,555× 663,669× 659,694× 694,504× 792,505× 873,962× 875,852× 708,102× 741,736× 452,439× 465,760× 550,356× 308,219× 236,260× 221,298× 165,066× 131,061× 59,559× 73,342× 104,298× 103,724× 145,724× 164,192× 158,888× 57,429× 83,881× 87,057× 105,344× 127,004× 130,052× 70,682× 74,189× 101,543× 143,662× 87,941× 40,055× 31,116× 38,353× 29,100× 108,427× 71,043× 24,782× 23,601× 16,650× 22,699× 45,165× 48,825× 69,692× 54,815× 44,432× 56,157× 45,422× 60,877× 52,238× 165,214× 40,060× 61,932× 72,937× 43,313× 43,773× 34,395× 13,099× 13,751× 31,387× 264× | 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: 1× 188,458× 490,275× 1,028,454× 1,660,662× 2,637,979× 3,839,449× 5,226,225× 6,855,822× 8,640,632× 9,041,315× 10,513,462× 12,279,237× 13,307,847× 12,800,256× 10,468,714× 8,612,117× 6,823,307× 5,715,295× 3,970,306× 3,331,982× 2,809,801× 2,047,438× 1,730,789× 1,923,424× 2,526,177× 2,454,675× 2,643,473× 2,339,361× 2,241,684× 2,029,574× 1,581,175× 1,045,539× 639,189× 480,820× 159,664× 58,502× | 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: 1× 954,246× 3,627,989× 15,193,398× 16,663,169× 17,901,779× 23,421,385× 19,695,353× 23,187,497× 24,021,989× 20,812,086× 17,264,040× 19,651,483× 18,031,029× 15,072,808× 11,512,506× 15,834,285× 14,698,109× 14,816,207× 15,363,768× 12,345,310× 15,642,889× 14,228,732× 12,546,862× 11,421,631× 14,967,685× 15,279,158× 15,571,575× 11,813,112× 10,750,149× 11,176,872× 12,840,603× 13,833,012× 11,477,299× 12,595,807× 14,239,413× 13,540,969× 14,674,425× 12,347,160× 11,036,486× 9,517,529× 10,694,278× 9,953,343× 11,727,189× 11,406,146× 10,266,857× 11,816,885× 14,714,309× 13,141,683× 11,679,755× 10,837,645× 11,698,608× 9,946,974× 8,848,539× 8,383,877× 7,455,601× 9,623,388× 9,954,942× 11,528,224× 12,531,862× 12,006,149× 11,776,734× 14,689,267× 12,390,301× 10,504,846× 11,980,805× 12,779,351× 14,756,032× 12,331,751× 12,685,349× 11,054,527× 11,603,296× 9,905,385× 9,007,682× 8,567,365× 8,678,538× 8,787,511× 7,732,060× 6,871,635× 6,313,554× 5,029,040× 6,045,807× 5,831,343× 5,039,734× 3,346,749× 3,398,104× 2,201,083× 2,208,683× 1,814,808× 1,476,327× 789,773× 787,029× 1,070,167× 863,684× 342,591× 18,820× | 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: 1× 3,202,038× 14,600,929× 35,489,249× 72,676,349× 118,687,438× 165,439,157× 235,445,333× 239,193,168× 300,087,112× 289,526,370× 274,284,023× 231,519,697× 188,128,480× 185,627,619× 173,369,685× 184,473,416× 174,968,995× 171,433,746× 142,129,385× 125,729,276× 98,404,939× 82,201,344× 77,025,152× 59,632,585× 68,554,720× 69,276,508× 85,869,791× 84,049,341× 105,834,231× 102,884,080× 93,332,359× 90,204,447× 90,159,325× 130,555,578× 135,536,249× 210,739,434× 214,782,617× 239,556,253× 216,916,208× 180,368,748× 158,836,116× 147,396,826× 108,471,625× 61,959,143× 42,570,714× 23,898,095× 19,896,710× 14,148,385× 9,661,719× 6,253,546× 2,754,519× 599,937× 59,340× |