| 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 Full Cycle | 1.97 step avg | 4.93 step avg | 8.50 step avg | 15.32 step avg | 11.56 step avg | 61.12 step avg | 13.56 step avg | 39.97 step avg | 24.80 step avg | 53.43 step avg | 80.38 step avg | 30.75 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 28× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 2× 47× 56× 52× 106× 60× 112× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 0× 1× 28× 449× 221× 440× 430× 416× 398× 376× 350× 320× 286× 248× 206× 160× 110× 56× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 0× 1× 28× 0× 0× 0× 0× 0× 594× 1,709× 513× 0× 0× 0× 0× 7,596× 22,266× 3,029× 224× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 0× 1× 28× 0× 0× 4,360× 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: 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× 28× 2,096× 7,009× 23,455× 14,098× 3,464× 7,812× 11,535× 12,754× 15,419× 12,025× 5,212× 3,211× 6,348× 9,826× 11,689× 11,704× 16,436× 12,381× 4,135× 4,077× 2,550× 1,812× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 23,275× 62,264× 120,450× 81,047× 58,826× 34,871× 43,619× 34,520× 37,483× 41,490× 41,739× 37,122× 35,573× 36,291× 33,348× 21,534× 26,271× 24,274× 26,913× 32,874× 39,466× 25,262× 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: 28s: 29s: 0× 1× 28× 15,512× 30,360× 110,276× 209,410× 280,369× 398,037× 463,137× 596,283× 618,872× 582,896× 487,183× 391,840× 285,920× 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: 62s: 63s: 64s: 65s: 66s: 67s: 68s: 69s: 70s: 71s: 72s: 73s: 74s: 75s: 76s: 77s: 0× 1× 28× 2,176× 5,744× 36,378× 72,552× 89,273× 55,428× 3,708× 2,336× 1,033× 15,925× 52,509× 264,535× 326,420× 254,256× 179,098× 329,864× 727,925× 798,906× 790,568× 843,734× 955,489× 895,690× 733,280× 680,127× 637,639× 611,571× 701,395× 580,769× 628,907× 494,267× 419,813× 396,383× 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: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 0× 1× 23,176× 90,689× 326,195× 398,566× 958,828× 1,042,054× 1,599,596× 1,634,414× 1,919,582× 2,278,685× 2,717,453× 3,206,302× 3,983,103× 4,225,197× 3,349,101× 3,772,089× 5,481,042× 6,821,947× 7,084,173× 6,811,066× 6,323,080× 5,189,783× 3,785,986× 2,561,874× 1,994,770× 1,653,943× 2,049,522× 2,295,644× 2,644,267× 2,402,316× 2,323,860× 1,966,716× 2,855,633× 3,211,951× 3,139,080× 3,398,611× 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: 85s: 86s: 87s: 88s: 89s: 90s: 91s: 92s: 93s: 94s: 95s: 96s: 97s: 98s: 99s: 100s: 101s: 102s: 103s: 104s: 105s: 106s: 0× 1× 28× 10,287× 54,442× 346,319× 781,380× 1,690,423× 2,597,234× 1,226,202× 2,053,035× 1,802,715× 1,340,641× 1,099,501× 1,197,235× 663,193× 414,007× 100,228× 96,999× 180,047× 40,629× 22,679× 0× 54,879× 372,314× 2,558,041× 7,021,116× 7,212,995× 8,871,209× 7,304,024× 8,339,431× 9,086,762× 9,013,508× 7,955,727× 8,179,084× 8,345,445× 9,058,282× 12,145,164× 10,849,483× 10,630,634× 10,014,048× 8,180,778× 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: 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: 0× 1× 28× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 1,737,388× 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: 69s: 70s: 71s: 0× 1× 28× 0× 53,445× 939,747× 5,908,118× 19,313,135× 27,720,373× 36,614,303× 45,189,761× 115,729,317× 171,336,405× 171,359,622× 181,376,218× 151,766,794× 153,445,605× 202,726,143× 179,121,726× 148,659,281× 126,076,368× 100,667,545× 126,521,680× 103,532,142× 82,620,350× 99,415,520× 116,803,622× 131,303,202× 90,829,339× 66,936,360× 76,853,760× 88,088,567× 135,727,542× 140,229,443× 131,055,323× 132,997,917× 129,293,331× 112,030,178× 119,727,631× 128,894,603× 142,889,465× 149,525,530× 130,402,198× 120,247,841× 117,973,422× 120,900,408× 145,652,573× 132,318,179× 96,213,955× 81,385,526× 73,702,354× 84,201,000× 67,067,855× 58,622,407× 43,463,784× 36,817,227× 26,789,554× 35,142,177× 19,662,270× 16,453,516× 14,577,629× 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× |