| 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 | 2.95 step avg | 7.65 step avg | 1.86 step avg | 8.55 step avg | 18.70 step avg | 13.17 step avg | 27.23 step avg | 13.71 step avg | 27.88 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 34× | 0s: 1s: 2s: 3s: 4s: 3× 108× 77× 170× 272× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 1× 681× 320× 638× 628× 614× 596× 574× 548× 518× 484× 446× 404× 358× 308× 254× 196× 134× 68× | 0s: 1s: 2s: 3s: 4s: 1× 17,170× 49,912× 6,409× 323× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 1× 7,474× 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: 1× 7,238× 13,546× 54,428× 214,377× 79,117× 85,788× 93,136× 62,602× 91,028× 150,738× 174,512× 133,133× 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: 1× 61,210× 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: 1× 63,193× 265,090× 1,204,652× 2,922,266× 3,055,479× 2,945,109× 3,743,269× 3,911,006× 3,731,227× 3,901,109× 3,583,597× 3,587,297× 3,912,858× 4,314,600× 4,189,844× 4,260,904× 3,758,776× 3,115,209× 3,519,588× 3,665,976× 3,092,656× 2,493,006× 1,728,222× 1,263,257× 1,175,907× 960,986× 974,741× 1,082,649× 1,133,510× 1,025,302× 1,171,633× 1,071,243× 1,020,399× 950,350× 823,897× 919,350× 841,599× 765,448× 891,144× 558,472× 434,213× 414,259× 606,540× 464,763× 468,817× 658,866× 889,192× 1,358,695× 1,196,337× 1,158,886× 1,670,398× 1,499,416× 1,088,119× 835,961× 1,212,654× 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: 1× 606,389× 2,652,769× 5,703,261× 10,730,316× 19,647,858× 25,740,008× 32,144,673× 33,277,996× 27,529,315× 27,659,533× 32,761,543× 37,789,441× 43,098,420× 42,974,864× 38,678,421× 28,955,177× 21,224,256× 20,558,921× 15,769,481× 13,720,231× 10,593,301× 12,005,993× 12,590,235× 8,973,429× 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: 1× 382,704× 3,074,342× 22,474,911× 41,953,841× 57,218,904× 58,647,858× 71,085,223× 81,036,713× 75,156,301× 76,327,148× 79,870,594× 69,752,600× 71,872,253× 80,903,299× 83,649,880× 91,189,633× 80,413,037× 77,258,599× 81,691,563× 76,642,885× 69,588,854× 58,926,677× 54,117,783× 54,106,968× 50,849,784× 41,839,043× 39,949,894× 34,489,338× 28,540,166× 23,748,802× 20,618,065× 24,454,022× 22,556,419× 20,687,952× 19,841,487× 13,401,382× 9,894,216× 11,505,191× 14,376,666× 16,023,930× 8,149,210× 9,149,483× 9,461,851× 13,276,888× 10,976,047× 12,768,089× 10,831,291× 6,187,776× 7,456,060× 13,271,396× 15,840,149× 14,573,055× 12,211,418× 7,523,532× 8,968,322× 8,967,686× 12,111,060× 13,536,294× 11,812,979× 20,676,177× 17,666,735× 19,523,475× 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× |