| 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 | 5.62 step avg | 11.92 step avg | 24.83 step avg | 14.54 step avg | 37.62 step avg | 22.82 step avg | 130.82 step avg | 27.65 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 46× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 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: 25s: 26s: 0× 1× 46× 1,151× 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: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 24s: 25s: 26s: 27s: 0× 1× 46× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 54,648× 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: 22s: 23s: 24s: 25s: 0× 1× 46× 0× 0× 17,344× 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: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 0× 1× 46× 0× 0× 0× 0× 0× 0× 0× 13,503× 27,067× 58,393× 67,054× 113,297× 170,452× 74,547× 75,002× 96,085× 97,771× 91,550× 87,196× 154,936× 429,998× 825,399× 718,400× 554,959× 802,780× 874,431× 1,253,792× 787,164× 684,124× 751,870× 754,937× 739,787× 832,527× 938,909× 917,353× 721,091× 762,619× 473,848× 478,376× 576,279× 317,207× 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: 37s: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 0× 1× 46× 0× 0× 0× 0× 0× 0× 188,412× 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: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 104s: 105s: 106s: 107s: 108s: 109s: 110s: 111s: 112s: 113s: 114s: 115s: 116s: 117s: 118s: 119s: 120s: 121s: 122s: 123s: 124s: 125s: 126s: 127s: 128s: 129s: 130s: 131s: 132s: 133s: 134s: 135s: 136s: 137s: 138s: 139s: 140s: 141s: 142s: 143s: 144s: 145s: 146s: 147s: 148s: 149s: 150s: 151s: 152s: 153s: 154s: 155s: 156s: 157s: 158s: 159s: 160s: 161s: 162s: 163s: 164s: 165s: 166s: 167s: 168s: 169s: 170s: 171s: 172s: 173s: 174s: 175s: 176s: 177s: 178s: 179s: 180s: 181s: 182s: 183s: 184s: 185s: 186s: 187s: 188s: 189s: 190s: 191s: 0× 1× 46× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 109,805× 436,896× 1,968,229× 2,256,303× 2,901,693× 2,543,324× 1,291,728× 2,198,846× 2,434,736× 1,819,037× 1,644,953× 758,014× 1,184,180× 1,351,229× 1,605,876× 1,877,947× 992,207× 1,225,065× 977,981× 514,591× 1,096,859× 804,506× 544,592× 540,745× 911,903× 3,006,062× 2,093,070× 1,353,473× 855,362× 1,168,302× 633,619× 439,577× 510,413× 336,152× 195,816× 446,900× 393,429× 456,494× 591,403× 419,667× 505,122× 586,012× 447,448× 227,534× 184,826× 128,123× 125,904× 37,292× 25,600× 20,474× 1,848× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 597,296× 2,361,605× 10,311,728× 12,478,468× 13,798,727× 20,042,961× 17,304,373× 20,424,619× 21,172,078× 18,532,022× 15,380,360× 18,758,809× 16,406,745× 13,333,518× 9,450,136× 13,364,935× 13,286,235× 13,086,020× 13,799,775× 11,383,271× 14,318,496× 13,239,400× 11,874,147× 11,002,081× 14,847,978× 15,160,937× 15,386,429× 11,659,150× 10,729,887× 11,107,822× 12,771,016× 13,808,610× 11,427,913× 12,498,382× 14,178,257× 13,534,173× 14,669,057× 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: 54s: 55s: 0× 1× 201,358× 1,208,675× 4,463,440× 10,051,242× 20,064,611× 35,503,461× 59,634,927× 84,200,352× 108,818,213× 131,256,879× 149,339,678× 172,862,423× 168,718,104× 154,152,210× 144,679,872× 132,922,642× 154,371,880× 161,629,830× 196,634,362× 208,237,990× 215,960,882× 245,273,558× 227,198,550× 198,793,244× 153,562,573× 128,420,865× 134,080,907× 157,521,305× 153,497,760× 171,764,150× 153,025,815× 127,565,133× 112,617,837× 101,175,209× 138,602,069× 142,372,262× 218,945,120× 223,194,629× 245,026,413× 219,453,598× 182,528,002× 162,502,870× 152,598,730× 111,452,823× 62,452,333× 42,591,012× 23,898,095× 19,896,710× 14,148,385× 9,661,719× 6,253,546× 2,754,519× 599,937× 59,340× |