| Radix Character Encoding | |||
|---|---|---|---|
| 0 | 1 | 2 | 3 |
| 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 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.75 step avg | 2.60 step avg | 2.75 step avg | 3.34 step avg | 4.30 step avg | 4.42 step avg | 4.34 step avg | 5.35 step avg | 4.37 step avg | 4.57 step avg | 4.51 step avg | 4.35 step avg | 4.10 step avg | 4.59 step avg | 4.09 step avg | 4.09 step avg | 4.09 step avg | 4.02 step avg | 3.94 step avg | 4.05 step avg | 3.92 step avg | 3.91 step avg | 3.93 step avg | 3.90 step avg | 3.86 step avg | 3.93 step avg | 3.83 step avg | 3.85 step avg | 3.86 step avg | 3.85 step avg | 3.80 step avg | 3.85 step avg | 3.79 step avg | 3.81 step avg | 3.81 step avg | 3.80 step avg | 3.76 step avg | 3.81 step avg | 3.76 step avg | 3.78 step avg | 3.77 step avg | 3.77 step avg | 3.74 step avg | 3.78 step avg | 3.74 step avg | 3.75 step avg | 3.74 step avg | 3.75 step avg | 3.72 step avg | 3.76 step avg | 3.72 step avg | 3.73 step avg | 3.72 step avg | 3.73 step avg | 3.71 step avg | 3.74 step avg | 3.71 step avg | 3.72 step avg | 3.71 step avg | 3.72 step avg | 3.70 step avg | 3.72 step avg | 3.70 step avg | 3.71 step avg | 3.70 step avg | 3.71 step avg | 3.69 step avg | 3.71 step avg | 3.69 step avg | 3.70 step avg | 3.69 step avg | 3.69 step avg | 3.68 step avg | 3.70 step avg | 3.68 step avg | 3.69 step avg | 3.68 step avg | 3.69 step avg | 3.67 step avg | 3.69 step avg | 3.67 step avg | 3.68 step avg | 3.67 step avg | 3.68 step avg | 3.67 step avg | 3.68 step avg | 3.67 step avg | 3.68 step avg | 3.67 step avg | 3.68 step avg | 3.66 step avg | 3.68 step avg | 3.66 step avg | 3.67 step avg | 3.66 step avg | 3.67 step avg | 3.66 step avg | 3.67 step avg | 3.66 step avg | 3.67 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 3× | 0s: 1s: 2s: 3s: 4s: 0× 1× 4× 3× 2× | 0s: 1s: 2s: 3s: 4s: 0× 1× 9× 4× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 0× 1× 6× 14× 8× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 0× 1× 3× 12× 18× 6× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 15× 8× 18× 14× 22× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 11× 28× 24× 28× 18× 10× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 12× 24× 42× 14× 14× 18× 22× 18× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 25× 42× 34× 72× 34× 12× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 23× 48× 64× 70× 56× 18× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 27× 74× 66× 104× 62× 30× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 40× 106× 108× 100× 64× 24× 12× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 43× 132× 170× 158× 50× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 45× 174× 166× 104× 88× 40× 44× 18× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 65× 184× 270× 218× 60× 18× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 64× 254× 320× 212× 96× 22× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 75× 328× 340× 244× 128× 18× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 89× 390× 416× 300× 100× 34× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 99× 434× 572× 336× 86× 12× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 102× 538× 558× 366× 162× 32× 12× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 129× 602× 738× 432× 94× 22× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 129× 738× 832× 438× 136× 20× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 147× 868× 876× 472× 196× 34× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 162× 958× 1,036× 572× 164× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 179× 1,058× 1,282× 596× 138× 16× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 183× 1,274× 1,244× 608× 270× 52× 22× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 217× 1,398× 1,532× 710× 158× 38× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 218× 1,608× 1,654× 734× 214× 50× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 243× 1,784× 1,784× 794× 288× 60× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 259× 1,948× 2,006× 914× 246× 66× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 283× 2,162× 2,328× 942× 210× 52× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 288× 2,488× 2,310× 950× 398× 100× 10× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 329× 2,680× 2,688× 1,122× 246× 68× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 331× 2,946× 2,932× 1,112× 346× 86× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 363× 3,222× 3,114× 1,222× 412× 90× 12× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 380× 3,526× 3,382× 1,354× 372× 108× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 0× 1× 411× 3,844× 3,828× 1,404× 298× 88× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 417× 4,288× 3,798× 1,436× 544× 142× 18× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 465× 4,522× 4,366× 1,658× 350× 102× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 468× 4,906× 4,672× 1,636× 490× 142× 20× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 507× 5,356× 4,890× 1,788× 556× 124× 16× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 525× 5,782× 5,258× 1,916× 534× 148× 20× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 563× 6,212× 5,794× 2,020× 452× 122× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 570× 6,740× 5,886× 2,032× 748× 200× 32× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 625× 7,086× 6,586× 2,314× 518× 150× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 629× 7,670× 6,930× 2,280× 696× 186× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 675× 8,268× 7,248× 2,466× 748× 178× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 694× 8,824× 7,668× 2,648× 750× 208× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 739× 9,324× 8,426× 2,792× 626× 176× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 747× 10,014× 8,548× 2,818× 980× 250× 46× 22× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 809× 10,562× 9,356× 3,152× 690× 202× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 814× 11,312× 9,808× 3,082× 888× 258× 56× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 867× 12,066× 10,176× 3,368× 966× 234× 36× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 887× 12,702× 10,822× 3,508× 974× 284× 66× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 939× 13,358× 11,720× 3,720× 830× 236× 46× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 948× 14,308× 11,840× 3,708× 1,258× 348× 82× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,017× 15,016× 12,836× 4,100× 926× 262× 56× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,023× 15,940× 13,332× 4,058× 1,204× 330× 86× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,083× 16,792× 13,914× 4,426× 1,232× 300× 66× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,104× 17,602× 14,662× 4,594× 1,280× 356× 96× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,163× 18,520× 15,668× 4,850× 1,078× 302× 76× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,173× 19,680× 15,872× 4,834× 1,558× 428× 124× 10× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,249× 20,556× 16,990× 5,352× 1,170× 350× 86× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,256× 21,588× 17,744× 5,236× 1,492× 450× 122× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,323× 22,640× 18,434× 5,696× 1,532× 388× 96× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,345× 23,738× 19,244× 5,836× 1,600× 482× 132× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,411× 24,860× 20,454× 6,126× 1,386× 390× 106× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,422× 26,238× 20,662× 6,138× 1,970× 554× 148× 22× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,505× 27,208× 22,098× 6,744× 1,528× 428× 122× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,513× 28,458× 22,954× 6,632× 1,930× 534× 158× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,587× 29,832× 23,712× 7,168× 1,920× 466× 132× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,610× 31,152× 24,686× 7,312× 2,026× 554× 168× 16× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 1,683× 32,486× 26,018× 7,734× 1,756× 474× 142× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 0× 1× 1,695× 34,000× 26,484× 7,682× 2,422× 636× 196× 18× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 1,785× 35,182× 28,108× 8,420× 1,888× 526× 150× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 1,794× 36,780× 29,018× 8,224× 2,356× 672× 208× 20× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 1,875× 38,402× 29,956× 8,842× 2,322× 586× 160× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 1,899× 39,952× 30,998× 9,006× 2,494× 726× 218× 20× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 1,979× 41,408× 32,680× 9,526× 2,164× 616× 170× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 1,992× 43,184× 33,216× 9,452× 2,942× 828× 234× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,089× 44,716× 34,980× 10,282× 2,344× 670× 186× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,099× 46,580× 36,062× 10,064× 2,892× 818× 228× 20× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,187× 48,458× 37,082× 10,856× 2,814× 730× 196× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,212× 50,140× 38,486× 10,978× 3,036× 872× 244× 20× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,299× 51,852× 40,364× 11,606× 2,632× 760× 206× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,313× 54,036× 40,914× 11,514× 3,490× 974× 284× 32× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,417× 55,828× 42,946× 12,418× 2,794× 832× 228× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,428× 57,966× 44,088× 12,214× 3,446× 1,028× 282× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,523× 59,994× 45,450× 13,118× 3,342× 892× 244× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,549× 61,950× 46,996× 13,220× 3,638× 1,082× 298× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,643× 64,072× 49,014× 13,932× 3,184× 922× 260× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,658× 66,566× 49,712× 13,778× 4,156× 1,192× 320× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,769× 68,626× 51,898× 14,886× 3,426× 982× 276× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,781× 70,924× 53,434× 14,576× 4,178× 1,184× 330× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,883× 73,252× 54,960× 15,652× 3,998× 1,042× 292× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 2,910× 75,644× 56,584× 15,718× 4,376× 1,238× 346× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 3,011× 78,070× 58,886× 16,520× 3,816× 1,072× 308× 10× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 3,027× 80,882× 59,604× 16,420× 4,926× 1,340× 382× 46× 22× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 3,145× 83,088× 62,236× 17,682× 4,046× 1,142× 328× 26× 6× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 3,158× 85,704× 63,914× 17,320× 4,888× 1,392× 402× 56× 16× |