| 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 | 10.53 step avg | 10.03 step avg | 19.30 step avg | 11.84 step avg | 35.97 step avg | 14.95 step avg | 47.30 step avg | 25.73 step avg | 39.93 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 36× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 0× 1× 36× 18× 0× 0× 0× 0× 0× 5× 166× 153× 324× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 0× 1× 36× 721× 357× 712× 702× 688× 670× 648× 622× 592× 558× 520× 478× 432× 382× 328× 270× 208× 142× 72× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 0× 1× 36× 0× 0× 0× 0× 0× 0× 0× 1,182× 4,185× 133× 0× 0× 0× 0× 0× 0× 20,136× 58,344× 7,013× 360× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 0× 1× 36× 0× 6,441× 17,638× 17,077× 21,864× 42,768× 63,239× 79,066× 88,036× 97,645× 79,159× 87,465× 54,689× 43,743× 28,271× 15,417× 5,765× 1,078× | 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: 0× 1× 36× 0× 0× 3,369× 4,202× 14,262× 23,221× 63,403× 69,438× 76,021× 93,856× 77,615× 72,277× 52,605× 52,149× 72,300× 96,038× 70,679× 78,536× 77,184× 93,151× 100,086× 104,138× 97,923× 78,056× 74,086× 86,930× 133,418× 214,070× 238,628× 203,162× 213,153× 165,046× 159,795× 162,196× 120,237× 125,631× 144,241× 146,565× 118,636× 96,220× 67,308× 44,329× 36,928× 45,051× 46,388× 63,305× 42,019× 49,516× 56,310× 54,348× 52,882× 45,456× 45,232× 35,108× 39,533× 36,342× 43,898× 37,997× 38,765× 28,307× 26,423× 36,176× 32,725× 29,172× 11,659× 15,097× 27,219× 31,539× 34,628× 45,690× 26,969× 6,781× 12,255× 18,543× 17,881× 16,885× 22,578× 12,603× 6,742× 3,573× 3,116× 9,308× 4,934× 3,593× 7,123× 955× 37× | 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: 0× 1× 36× 38,628× 96,592× 289,504× 543,750× 907,339× 1,182,909× 1,399,197× 2,207,512× 2,666,528× 2,993,562× 3,155,964× 2,803,924× 2,055,004× 1,349,000× 1,197,387× 930,320× 870,198× 874,822× 1,265,035× 1,355,412× 1,209,917× 756,360× 692,410× 583,083× 426,541× 242,644× 72,100× 42,582× 12,883× 2,970× | 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: 0× 1× 36× 8,624× 42,736× 210,310× 267,825× 333,042× 384,756× 505,908× 673,108× 1,033,986× 868,769× 1,307,074× 1,413,876× 1,756,678× 1,384,354× 1,430,144× 1,704,237× 1,954,040× 1,570,204× 2,241,440× 1,736,786× 2,080,437× 2,051,847× 1,966,975× 2,386,428× 2,178,183× 2,334,255× 1,507,282× 1,272,943× 1,302,931× 1,077,430× 1,667,935× 1,609,578× 1,287,951× 1,172,785× 1,383,264× 2,022,110× 1,956,695× 1,685,933× 2,035,796× 2,351,340× 2,438,190× 2,350,950× 2,318,482× 2,330,071× 3,753,794× 4,886,977× 4,607,259× 5,107,625× 7,504,191× 6,756,109× 6,217,621× 5,938,476× 5,839,675× 4,841,331× 4,515,153× 4,133,733× 3,596,630× 4,292,161× 4,519,054× 4,835,142× 4,509,687× 4,143,952× 3,381,226× 2,427,008× 2,066,161× 1,957,001× 1,144,123× 1,182,113× 1,255,959× 1,137,766× 944,389× 1,003,530× 805,156× 924,104× 782,843× 741,715× 685,582× 287,194× 376,003× 219,151× 203,965× 49,931× 37,672× 23,740× | 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: 0× 1× 35,876× 288,457× 912,969× 2,233,997× 4,788,461× 8,099,653× 13,488,058× 17,618,976× 21,146,401× 28,313,175× 33,537,986× 35,458,898× 31,744,705× 27,797,404× 22,994,293× 20,331,145× 22,000,900× 22,773,640× 28,827,169× 36,592,768× 36,175,464× 30,053,104× 21,070,877× 15,337,259× 10,408,557× 8,944,980× 9,728,273× 13,741,896× 14,223,105× 14,954,809× 12,399,196× 15,518,562× 18,426,681× 22,441,301× 28,246,579× 27,948,770× 34,245,967× 32,770,643× 36,246,117× 32,006,907× 27,305,354× 17,838,055× 11,402,190× 7,805,952× 5,064,313× 2,063,872× 618,855× 168,777× 21,788× | 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: 0× 1× 36× 18,872× 261,264× 1,873,365× 4,547,136× 10,649,321× 8,193,885× 8,406,917× 10,378,398× 20,509,443× 32,876,703× 37,612,255× 34,200,513× 38,632,453× 27,092,017× 29,097,876× 23,875,564× 22,829,371× 31,488,558× 37,567,373× 32,804,078× 44,854,149× 63,242,954× 71,737,559× 89,948,451× 107,291,987× 92,408,506× 107,605,380× 97,866,881× 92,326,129× 88,522,222× 85,969,010× 88,554,037× 76,963,260× 73,513,533× 69,222,629× 81,416,939× 72,266,413× 63,516,651× 84,847,103× 131,651,566× 135,567,956× 128,357,799× 142,732,255× 123,809,859× 131,901,228× 147,050,412× 124,356,275× 128,705,436× 118,606,589× 121,816,608× 98,007,143× 88,896,776× 80,337,724× 66,127,189× 50,506,435× 43,755,474× 34,113,931× 32,154,604× 31,450,927× 27,100,057× 18,262,365× 18,581,608× 13,091,880× 11,999,605× 10,439,319× 8,838,773× 10,559,984× 10,974,271× 8,535,526× 4,828,523× 2,547,454× 1,156,488× 1,125,185× 535,444× 1,173,693× 763,265× 596,959× 222,310× 37,917× 59,984× 10,795× 1,873× 1,137× 10,628× |