| 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 |
|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.97 step avg | 3.79 step avg | 8.41 step avg | 1.85 step avg | 11.39 step avg | 25.59 step avg | 13.42 step avg | 52.65 step avg | 13.98 step avg | 51.81 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 38× | 0s: 1s: 2s: 3s: 4s: 5s: 2× 83× 49× 114× 228× 304× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 1× 837× 396× 790× 780× 766× 748× 726× 700× 670× 636× 598× 556× 510× 460× 406× 348× 286× 220× 150× 76× | 0s: 1s: 2s: 3s: 4s: 1× 26,258× 76,551× 8,721× 399× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 1× 2,586× 4,411× 6,802× 15,162× 24,388× 43,016× 63,629× 74,743× 68,589× 97,822× 95,001× 86,467× 88,032× 79,989× 62,293× 54,987× 43,678× 29,381× 15,136× 5,290× 1,195× | 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: 1× 17,936× 47,546× 96,224× 189,854× 278,397× 185,544× 152,393× 168,510× 96,516× 81,876× 83,558× 73,894× 77,875× 68,829× 74,069× 168,708× 170,683× 221,063× 273,373× 181,396× 169,628× 187,340× 160,505× 217,616× 344,325× 243,028× 158,218× 173,571× 100,792× 77,086× 85,559× 154,121× 147,124× 134,863× 105,195× 162,086× 124,710× 114,198× 169,433× 141,642× 102,316× 74,120× 103,278× 78,809× 100,632× 86,439× 87,031× 67,981× 74,844× 76,191× 71,375× 71,831× 77,844× 59,841× 19,007× 16,271× 6,325× 1,467× 1,482× 2,683× | 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× 92,410× 240,755× 445,480× 829,572× 1,225,844× 1,720,384× 2,135,241× 2,584,665× 3,002,050× 3,499,128× 3,713,175× 3,979,069× 4,449,483× 3,358,239× 2,683,515× 1,692,764× 1,184,905× 755,123× 540,825× 407,126× 363,301× 539,514× 636,809× 763,417× 965,108× 1,009,430× 755,274× 453,982× 416,320× 440,054× 292,934× 150,010× 45,998× 4,100× 3,615× | 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: 1× 211,821× 874,775× 3,572,864× 3,757,665× 3,738,095× 2,608,956× 3,002,714× 3,712,868× 4,619,723× 3,949,860× 3,106,539× 2,474,375× 1,882,099× 1,645,435× 2,124,305× 1,626,072× 1,877,953× 1,799,074× 1,358,609× 2,205,783× 2,078,016× 2,087,952× 1,897,872× 2,482,844× 2,271,100× 1,766,881× 1,451,821× 1,301,512× 1,543,359× 1,186,457× 1,106,067× 1,292,794× 1,697,814× 1,386,632× 1,283,685× 1,184,099× 1,236,749× 1,907,378× 1,753,665× 1,834,465× 1,563,738× 2,426,365× 2,735,535× 3,550,867× 4,043,969× 4,731,229× 4,717,483× 4,405,531× 4,650,722× 3,714,967× 4,627,981× 4,459,559× 3,450,975× 3,572,896× 4,468,615× 4,085,370× 3,643,222× 2,812,198× 3,466,220× 3,653,806× 3,319,158× 3,104,156× 3,102,530× 2,713,679× 2,535,553× 2,629,576× 2,956,170× 2,418,546× 1,946,489× 2,176,231× 2,856,685× 2,816,843× 3,119,738× 3,421,988× 3,371,289× 2,861,204× 2,986,681× 2,552,414× 2,898,293× 2,943,767× 2,791,562× 1,748,870× 1,912,957× 1,589,255× 2,062,329× 2,000,143× 1,816,166× 1,178,890× 1,106,608× 936,065× 869,594× 761,392× 776,019× 1,802,290× 2,064,097× 2,518,492× 1,914,792× 1,611,971× 1,896,918× 1,708,183× 1,452,174× 1,100,049× 971,004× 1,133,402× 866,102× 528,326× 477,198× 840,736× 597,052× 509,203× 735,213× 597,831× 263,515× 159,892× 305,542× 383,936× 200,494× 263,127× 138,593× 154,997× 196,589× 209,525× 242,038× 53,366× 7,513× 43,765× 251,836× 270,686× 172,774× 130,757× 64,336× 55,164× 43,160× 2,809× 19,198× 1,148× 6,636× 2,890× 660× | 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× 1,183,381× 5,711,663× 13,642,654× 26,043,918× 48,187,777× 62,563,134× 84,594,553× 84,194,022× 81,089,379× 79,974,843× 70,041,698× 66,711,848× 60,793,836× 60,588,843× 59,222,446× 54,097,239× 64,084,889× 60,964,582× 69,420,881× 66,580,919× 60,050,454× 47,883,167× 38,736,936× 32,402,333× 21,433,833× 16,799,712× 11,966,595× 5,706,400× 2,236,676× 2,135,582× 2,254,968× 1,063,126× 246,249× 32,868× 7,740× | 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: 1× 1,769,365× 12,751,260× 83,160,304× 92,907,126× 113,211,518× 106,785,143× 107,848,364× 92,019,214× 84,880,693× 84,493,160× 84,667,715× 75,947,501× 63,671,734× 59,604,314× 48,741,795× 60,754,462× 66,282,123× 65,144,008× 70,948,644× 74,790,239× 73,545,793× 80,410,743× 88,930,514× 77,589,802× 75,366,157× 82,365,639× 76,468,283× 82,958,612× 75,144,042× 69,507,154× 62,521,991× 74,178,968× 85,927,667× 72,733,923× 54,812,265× 50,371,065× 59,142,229× 43,790,114× 33,329,469× 38,177,585× 40,300,529× 43,758,712× 44,129,903× 47,591,117× 53,576,426× 57,112,689× 61,283,383× 69,660,932× 75,570,742× 77,765,370× 85,018,816× 68,491,611× 55,295,810× 51,293,448× 43,954,376× 56,211,384× 56,633,694× 45,603,156× 38,642,864× 36,858,978× 37,437,927× 45,951,665× 51,358,755× 54,700,969× 55,482,621× 79,794,311× 78,893,579× 76,527,531× 66,937,367× 61,609,618× 65,933,177× 69,679,968× 76,850,144× 66,731,762× 61,944,354× 69,573,528× 67,007,265× 62,026,580× 54,484,251× 66,666,403× 73,565,951× 46,729,115× 48,980,009× 54,231,064× 60,534,689× 50,612,078× 46,331,082× 45,314,527× 49,497,443× 45,173,993× 31,304,728× 26,123,234× 20,230,505× 19,106,754× 26,382,491× 26,672,373× 25,731,362× 26,787,592× 27,564,140× 24,193,285× 19,780,748× 15,954,982× 19,651,021× 24,110,244× 27,128,558× 29,001,764× 16,014,035× 18,062,086× 15,191,879× 10,258,028× 9,421,353× 7,722,545× 8,524,709× 8,665,430× 7,441,726× 8,929,702× 9,371,634× 10,417,197× 18,980,080× 11,118,742× 9,735,168× 11,022,501× 10,377,888× 12,430,189× 22,023,772× 24,255,614× 26,574,414× 24,514,039× 20,311,259× 18,999,839× 14,836,413× 14,993,597× 9,543,967× 8,409,295× 4,491,474× 4,274,425× 5,481,081× 6,905,637× 5,651,124× 4,634,595× 6,529,905× 3,701,542× 1,804,135× 1,132,952× 545,704× 228,413× 761,759× 3,021,894× 1,029,429× 1,011,680× 210,986× 127,312× 240,207× 993,804× 2,910,716× 158,988× 30,888× |