| 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 Full Cycle | 1.97 step avg | 5.25 step avg | 9.65 step avg | 13.05 step avg | 12.55 step avg | 24.48 step avg | 21.17 step avg | 32.44 step avg | 28.92 step avg | 33.43 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 34× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 2× 56× 29× 120× 117× 102× 204× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 0× 1× 34× 647× 320× 638× 628× 614× 596× 574× 548× 518× 484× 446× 404× 358× 308× 254× 196× 134× 68× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 244× 329× 540× 1,005× 0× 1,686× 4,134× 753× 0× 0× 0× 14,700× 44,444× 5,656× 323× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 0× 1× 34× 0× 0× 7,440× 11,578× 12,740× 29,516× 47,081× 59,456× 60,778× 66,651× 60,480× 61,100× 52,786× 33,454× 23,597× 16,022× 16,747× 11,934× 4,362× | 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: 0× 1× 1,186× 2,416× 9,584× 48,004× 19,829× 21,184× 28,915× 49,814× 179,217× 72,472× 85,992× 82,076× 57,632× 78,184× 137,554× 159,176× 126,408× 122,661× 114,664× 170,343× 157,683× 132,843× 129,488× 129,383× 149,638× 171,780× 124,394× 99,456× 104,777× 106,046× 127,811× 91,667× 47,424× 69,632× 88,623× 105,833× 92,835× 74,762× 56,268× 20,161× 30,182× 30,061× 33,607× 21,040× 14,112× 9,966× 11,151× 8,116× 11,905× 11,656× 4,674× 4,094× | 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: 0× 1× 34× 0× 0× 0× 0× 0× 0× 61,176× 151,608× 345,799× 549,743× 800,463× 1,071,024× 1,180,173× 1,306,515× 1,575,791× 1,868,406× 1,933,666× 1,757,823× 1,694,718× 1,292,559× 975,129× 680,083× 547,448× 451,364× 323,429× 241,542× 241,407× 312,096× 316,645× 447,655× 516,275× 583,355× 329,610× 309,734× 234,873× 199,448× 95,194× 75,989× 8,106× 3,059× | 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× 34× 3,700× 22,448× 77,915× 333,125× 1,037,727× 1,642,924× 1,453,736× 1,629,330× 2,171,463× 1,929,456× 1,828,597× 2,192,826× 2,647,207× 3,619,035× 4,483,102× 4,626,961× 4,960,917× 5,105,260× 4,769,396× 4,449,432× 4,679,562× 4,539,557× 3,723,444× 2,876,885× 2,400,237× 1,817,072× 1,690,764× 1,441,209× 1,249,096× 1,512,107× 1,457,349× 1,212,630× 1,126,628× 1,054,463× 1,100,179× 879,166× 932,206× 1,220,055× 1,164,888× 1,108,511× 988,663× 624,569× 534,700× 642,994× 478,856× 436,379× 678,893× 910,569× 1,377,981× 1,226,027× 1,141,799× 1,672,733× 1,505,537× 1,107,493× 840,534× 1,213,610× 1,292,348× 1,326,450× 938,812× 846,563× 852,666× 1,302,169× 1,092,183× 815,282× 785,332× 399,857× 374,478× 566,223× 690,150× 711,803× 619,612× 287,038× 177,832× 247,165× 514,583× 539,181× 319,883× 129,918× 86,752× 215,793× 116,615× 310,957× 256,636× 100,284× 131,441× 116,406× 53,763× 49,963× 53,695× 64,778× 60,647× 26,633× 4,357× | 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: 0× 1× 53,402× 249,844× 776,368× 1,749,346× 4,067,732× 6,057,563× 8,351,010× 9,519,327× 9,031,019× 10,463,147× 13,595,495× 17,783,672× 19,611,288× 22,102,816× 17,497,525× 13,145,018× 5,634,574× 2,024,108× 896,173× 301,694× 634,527× 2,508,657× 5,054,749× 9,002,901× 15,580,126× 19,682,445× 23,793,663× 23,758,669× 18,498,296× 17,196,386× 19,166,048× 20,005,769× 23,487,132× 20,872,048× 21,180,896× 15,810,159× 15,589,682× 18,534,813× 14,873,308× 13,418,537× 10,511,761× 11,900,261× 12,462,379× 8,951,498× 5,939,862× 5,720,177× 6,915,823× 5,337,407× 5,217,064× 2,649,483× 2,869,680× 2,128,964× 959,271× 527,996× 260,964× 9,472× | 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: 0× 1× 34× 23,472× 175,547× 1,513,995× 4,327,860× 10,324,811× 22,323,510× 26,034,924× 28,125,823× 34,065,745× 40,949,052× 44,131,760× 47,374,502× 54,197,218× 69,393,590× 85,308,799× 83,668,474× 86,978,192× 96,547,085× 85,377,443× 77,662,168× 80,705,797× 76,979,920× 71,963,879× 68,187,717× 69,018,544× 73,606,844× 67,107,778× 60,312,906× 67,286,925× 60,715,400× 46,910,761× 38,583,966× 35,286,672× 37,877,811× 34,540,514× 25,937,294× 20,460,995× 15,022,347× 15,717,885× 18,667,652× 14,520,944× 11,124,653× 11,948,706× 12,510,083× 13,166,126× 13,953,274× 11,373,198× 6,587,498× 7,585,805× 14,510,790× 16,621,799× 16,019,151× 14,080,674× 10,339,363× 10,052,710× 9,700,426× 12,686,784× 13,834,272× 12,322,732× 21,116,457× 17,937,953× 19,668,891× 24,397,693× 21,764,419× 18,816,248× 18,391,248× 17,283,666× 21,219,623× 19,799,428× 16,433,201× 12,859,513× 13,713,667× 11,280,520× 10,420,217× 10,491,125× 9,381,575× 9,294,175× 5,543,027× 8,415,243× 7,208,864× 4,899,611× 4,620,800× 5,998,996× 6,092,798× 5,700,258× 3,019,840× 3,243,346× 3,094,936× 1,980,643× 1,861,425× 2,171,495× 4,674,603× 1,167,134× 311,219× 263,404× 148,077× 43,552× 42,746× 47,668× 41,396× 13,561× 46,623× 1,294× |