| 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 |
| 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 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.97 step avg | 2.13 step avg | 6.51 step avg | 1.88 step avg | 7.56 step avg | 13.12 step avg | 11.41 step avg | 24.49 step avg | 14.57 step avg | 32.06 step avg | 18.38 step avg | 24.19 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 28× | 0s: 1s: 2s: 3s: 5× 129× 105× 196× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 1× 477× 221× 440× 430× 416× 398× 376× 350× 320× 286× 248× 206× 160× 110× 56× | 0s: 1s: 2s: 3s: 4s: 1× 8,218× 23,975× 3,542× 224× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 1× 4,388× 7,278× 7,640× 16,935× 25,908× 31,759× 30,176× 28,409× 25,279× 17,712× 13,472× 8,858× 9,787× 7,254× 2,480× | 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: 1× 25,399× 69,273× 143,905× 95,145× 62,290× 42,683× 55,154× 47,274× 52,902× 53,515× 46,951× 40,333× 41,921× 46,117× 45,037× 33,238× 42,707× 36,655× 31,048× 36,951× 42,016× 27,074× 24,026× 16,973× 25,232× 30,868× 13,033× 14,443× 11,635× 11,440× 8,048× 5,414× 8,094× 5,337× 9,044× 10,259× 3,470× 7,504× 5,647× 5,542× 1,990× 2,750× 2,778× 1,707× 596× 432× 125× 836× 92× | 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: 1× 30,968× 52,772× 127,252× 247,362× 314,280× 441,953× 486,847× 556,409× 561,142× 522,450× 455,238× 387,880× 285,570× 286,387× 301,869× 275,677× 307,168× 295,729× 302,435× 214,612× 116,353× 59,077× 67,856× 11,718× 12,922× 1,648× 945× | 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: 1× 40,688× 149,063× 747,885× 1,022,350× 962,089× 941,173× 1,064,205× 1,077,923× 866,690× 813,265× 744,795× 740,705× 802,311× 623,920× 668,531× 500,885× 424,725× 396,523× 494,426× 441,564× 529,157× 567,336× 582,358× 357,820× 540,153× 453,131× 250,914× 293,654× 404,262× 590,371× 560,654× 914,443× 958,790× 761,113× 715,439× 348,803× 383,796× 349,716× 647,952× 853,834× 747,778× 795,546× 701,211× 507,472× 373,431× 415,528× 344,180× 359,338× 336,633× 176,928× 165,300× 94,164× 107,550× 130,855× 147,125× 46,208× 63,877× 83,582× 54,950× 18,079× 3,192× | 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: 1× 306,124× 1,167,118× 2,422,253× 3,536,189× 5,053,041× 6,669,109× 7,458,804× 8,707,006× 8,317,011× 7,055,065× 6,758,845× 5,709,816× 5,790,078× 4,226,220× 3,759,162× 3,332,926× 3,564,491× 3,417,758× 3,160,855× 2,370,902× 2,949,075× 3,229,663× 3,154,339× 3,404,444× 2,716,222× 3,110,581× 2,882,613× 2,194,566× 1,476,277× 1,203,352× 937,602× 477,910× 531,086× 438,303× 488,805× 782,020× 498,808× 711,522× 295,155× 97,806× 27,352× 5,148× 4,800× 2,072× 1,325× | 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: 1× 119,765× 777,766× 3,719,382× 8,584,239× 9,679,211× 11,605,895× 8,796,247× 9,154,342× 10,181,467× 9,757,426× 8,980,539× 9,078,020× 8,979,105× 9,447,230× 12,227,666× 10,898,457× 10,712,115× 10,029,782× 8,181,494× 9,202,998× 7,935,185× 7,423,640× 6,489,098× 6,230,829× 5,443,269× 5,348,972× 7,221,247× 7,051,799× 4,987,687× 5,366,502× 5,936,354× 5,446,354× 5,610,079× 5,983,401× 5,606,215× 4,330,881× 5,441,176× 10,172,397× 11,092,473× 9,013,242× 7,474,600× 8,848,446× 8,265,211× 7,671,383× 7,595,000× 5,130,978× 4,827,654× 9,022,493× 8,043,256× 8,769,548× 8,340,399× 8,781,477× 6,977,139× 6,291,436× 4,073,135× 4,626,220× 5,260,143× 4,071,563× 4,270,351× 4,741,434× 4,644,383× 4,709,403× 3,288,202× 2,291,384× 2,841,397× 2,818,577× 3,090,576× 2,973,093× 2,869,205× 1,865,898× 1,424,585× 1,031,540× 1,462,001× 935,586× 539,336× 235,136× 64,333× 83,505× 64,309× 56,683× 67,812× 31,534× 10,825× 8,640× | 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: 1× 1,737,416× 10,005,261× 26,879,264× 41,365,924× 56,681,345× 71,047,897× 68,866,108× 60,881,950× 58,968,891× 59,753,462× 69,389,399× 58,059,849× 57,375,381× 55,297,230× 58,180,442× 65,889,029× 66,298,245× 66,166,432× 64,708,959× 58,510,554× 58,217,205× 45,178,531× 39,832,020× 33,038,577× 26,001,846× 23,688,422× 29,497,049× 24,034,618× 20,145,756× 21,577,380× 24,161,071× 26,502,392× 27,442,483× 28,149,671× 24,568,741× 22,178,665× 22,056,829× 20,181,713× 18,830,809× 13,816,863× 10,501,571× 9,585,437× 8,643,012× 7,654,315× 4,818,729× 2,424,789× 1,231,770× 1,816,005× 2,761,674× 1,008,083× 391,505× 55,474× | 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: 1× 157,219× 2,214,279× 19,564,664× 79,109,649× 111,463,817× 132,848,507× 109,658,482× 194,845,432× 223,997,454× 231,532,092× 228,561,284× 185,584,009× 173,179,395× 192,512,537× 177,915,817× 167,632,515× 161,195,348× 129,323,844× 136,397,875× 125,998,541× 122,955,086× 119,957,957× 120,170,376× 120,380,755× 85,998,328× 51,879,629× 63,445,657× 62,935,718× 82,874,943× 87,142,849× 85,720,956× 100,833,216× 86,753,767× 67,778,700× 73,954,093× 70,625,085× 82,875,680× 100,690,448× 91,964,864× 91,336,457× 88,422,820× 85,269,309× 117,560,224× 116,087,148× 83,034,387× 66,251,503× 66,135,578× 79,311,525× 64,284,346× 56,751,039× 42,810,280× 35,295,559× 25,567,258× 34,608,018× 19,299,975× 16,019,216× 14,197,805× 10,806,477× 5,338,644× 2,507,043× 727,681× 1,037,984× 191,808× 474,680× 426,960× 343,076× 14,256× 111,556× |