| 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 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.97 step avg | 2.15 step avg | 7.27 step avg | 1.87 step avg | 10.48 step avg | 14.60 step avg | 12.44 step avg | 27.33 step avg | 15.04 step avg | 36.95 step avg | 22.32 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 32× | 0s: 1s: 2s: 3s: 5× 164× 136× 256× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 1× 609× 285× 568× 558× 544× 526× 504× 478× 448× 414× 376× 334× 288× 238× 184× 126× 64× | 0s: 1s: 2s: 3s: 4s: 1× 13,632× 39,848× 5,136× 288× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 1× 1,616× 2,897× 4,346× 9,674× 17,005× 23,339× 34,356× 42,431× 35,405× 40,772× 49,550× 42,482× 38,090× 34,302× 26,620× 18,077× 10,080× 3,928× 926× | 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× 3,120× 12,586× 36,350× 23,130× 22,100× 41,505× 78,923× 115,119× 189,594× 119,140× 104,734× 199,039× 234,667× 299,489× 368,522× 128,661× 129,062× 83,933× 92,218× 74,182× 78,353× 56,155× 45,710× 42,465× 37,796× 25,562× 29,187× 24,240× 21,691× 16,723× 10,924× 3,934× 2,566× 4,056× 5,244× | 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: 1× 50,192× 97,804× 246,078× 445,552× 606,090× 775,550× 884,483× 1,032,875× 1,140,990× 1,211,601× 1,315,419× 1,074,574× 900,483× 591,615× 432,184× 391,126× 513,823× 554,402× 751,973× 828,112× 641,488× 378,721× 223,716× 77,921× 76,307× 50,944× 48,336× 27,740× 10,837× | 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: 1× 93,524× 356,451× 1,253,085× 1,421,725× 1,366,295× 1,029,999× 1,248,498× 1,403,158× 1,053,727× 921,682× 1,378,634× 2,685,518× 4,645,423× 4,630,236× 2,323,078× 1,624,861× 1,825,877× 1,559,234× 1,420,646× 1,373,985× 1,490,056× 1,763,103× 949,114× 960,703× 1,118,617× 1,100,447× 990,683× 1,450,720× 1,099,389× 1,202,907× 1,400,647× 2,035,517× 1,445,857× 1,793,408× 1,182,936× 714,496× 795,940× 1,464,610× 2,025,019× 1,957,214× 1,687,123× 753,194× 771,952× 900,745× 1,177,811× 729,535× 707,748× 619,136× 447,430× 351,867× 443,979× 293,721× 247,319× 336,651× 397,947× 901,344× 430,134× 378,543× 364,357× 278,673× 594,326× 314,900× 222,523× 336,975× 718,112× 870,353× 185,910× 199,109× 174,793× 254,974× 93,624× 37,850× 27,947× 32,342× 62,486× 2,232× | 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: 1× 346,788× 1,660,134× 4,253,093× 8,163,345× 13,032,395× 19,212,468× 22,036,790× 25,294,086× 28,328,179× 25,076,186× 21,310,307× 15,575,991× 14,704,367× 10,534,620× 9,681,790× 8,188,909× 8,319,210× 9,450,306× 9,977,565× 10,979,745× 7,795,745× 5,844,877× 4,685,787× 4,454,255× 5,906,233× 6,375,971× 8,434,734× 7,099,852× 5,829,924× 3,425,472× 1,720,073× 1,767,174× 2,498,279× 2,925,683× 2,639,460× 1,064,057× 652,506× 753,556× 1,116,952× 1,984,951× 3,004,133× 2,378,301× 1,110,915× 379,297× 246,462× 119,859× 2,782× | 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: 1× 658,359× 4,906,115× 18,473,115× 31,976,966× 33,609,634× 39,297,929× 43,644,926× 41,767,275× 37,777,755× 30,126,364× 30,033,436× 33,919,075× 52,206,957× 36,575,506× 32,196,970× 32,679,073× 22,271,767× 24,500,003× 27,529,165× 53,928,673× 50,454,247× 24,780,179× 22,731,064× 26,801,339× 25,921,178× 32,239,148× 27,103,223× 20,886,721× 24,200,915× 19,778,450× 19,100,102× 19,485,810× 24,510,305× 18,952,361× 17,186,158× 11,715,757× 13,247,319× 15,793,258× 17,186,356× 13,469,926× 10,183,198× 7,715,421× 6,820,347× 3,444,693× 3,557,220× 3,195,458× 1,872,047× 3,188,651× 2,317,525× 4,070,260× 2,140,580× 2,290,654× 3,778,613× 2,052,825× 1,433,828× 1,475,847× 2,011,989× 4,501,609× 16,751,679× 11,949,947× 6,818,341× 5,013,833× 7,085,823× 7,277,026× 12,755,508× 8,152,582× 5,020,834× 4,723,119× 8,003,698× 6,005,766× 2,813,920× 2,062,640× 3,657,945× 3,716,607× 1,400,584× 3,545,084× 4,888,455× 8,840,040× 4,456,109× 2,889,833× 4,510,525× 2,038,431× 1,422,006× 2,577,830× 3,519,218× 1,787,971× 1,377,570× 1,011,545× 2,093,998× 1,146,048× 1,610,171× 1,293,847× 4,448,824× 2,087,720× 2,142,978× 1,929,360× 3,323,923× 6,307,005× 3,529,617× 2,132,687× 994,992× 1,402,170× 3,788,719× 3,151,944× 3,379,766× 1,942,638× 1,635,570× 912,186× 906,466× 3,750,368× 14,959,354× 5,656,687× 3,915,869× 3,986,214× 3,442,190× 6,571,239× 4,825,451× 3,312,600× 6,961,925× 5,160,354× 2,191,618× 1,479,746× 1,308,885× 2,853,635× 7,088,329× 2,367,191× 2,108,239× 3,697,557× 5,671,333× 9,776,275× 3,592,227× 3,198,533× 1,939,954× 844,899× 1,731,361× 844,580× 1,181,062× 1,289,703× 944,778× 900,284× 825,032× 1,002,840× 1,652,229× 911,946× 507,903× 1,271,997× 621,647× 214,273× 190,159× 618,068× 144,900× 20,796× | 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: 1× 2,978,626× 17,683,753× 48,082,517× 85,422,068× 141,064,547× 218,426,097× 266,386,033× 272,796,062× 227,180,210× 209,784,685× 187,153,239× 178,162,131× 144,092,146× 126,490,905× 108,640,335× 114,120,138× 117,140,431× 129,050,349× 149,098,119× 151,993,062× 160,640,218× 178,346,455× 185,794,906× 166,714,541× 144,982,860× 121,703,685× 112,970,571× 94,761,307× 101,075,350× 96,195,062× 90,987,260× 79,797,835× 73,773,741× 65,303,062× 72,870,664× 79,336,468× 85,464,269× 79,341,165× 74,841,939× 70,704,435× 55,469,182× 57,211,665× 55,879,878× 66,477,495× 65,002,223× 69,609,659× 57,191,620× 38,676,425× 24,848,279× 19,584,847× 19,141,323× 31,508,234× 27,769,616× 20,232,625× 11,188,517× 11,073,192× 8,899,698× 5,727,077× 3,831,185× 4,656,949× 3,730,652× 4,062,677× 5,732,910× 17,381,629× 17,653,202× 10,969,185× 4,300,804× 2,093,890× 478,582× 217,610× 52,272× |