| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.97 step avg | 1.44 step avg | 7.59 step avg | 4.25 step avg | 8.08 step avg | 14.79 step avg | 7.90 step avg | 16.58 step avg | 15.42 step avg | 14.12 step avg | 30.22 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 31× | 0s: 1s: 2s: 9× 279× 240× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 1× 303× 270× 538× 530× 518× 502× 482× 458× 430× 398× 362× 322× 278× 230× 178× 122× 62× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 1,979× 4,165× 9,109× 15,796× 11,680× 4,046× 5,584× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 1× 6,577× 9,548× 9,986× 21,916× 33,964× 46,448× 45,266× 43,534× 37,506× 37,376× 27,208× 17,630× 14,222× 11,786× 8,540× 4,946× 538× | 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: 1× 38,289× 101,628× 87,222× 46,059× 52,378× 62,165× 59,468× 81,804× 58,100× 82,336× 122,816× 121,698× 151,713× 104,077× 88,981× 99,904× 125,264× 109,471× 76,955× 69,387× 73,758× 98,057× 91,217× 86,219× 43,735× 46,359× 27,489× 28,702× 25,730× 9,426× 14,626× 9,366× 14,312× 7,344× 4,362× 4,158× 208× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 1× 111,279× 264,904× 519,188× 776,014× 1,092,120× 1,216,370× 1,497,378× 1,641,588× 1,799,316× 1,413,390× 1,042,206× 565,196× 313,124× 194,810× 107,254× 56,860× 7,060× 2,198× | 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: 1× 381,253× 1,901,117× 2,166,398× 1,601,198× 1,410,382× 1,348,169× 1,731,533× 2,041,845× 2,451,997× 2,278,299× 2,025,570× 2,464,462× 3,058,221× 3,009,475× 2,633,700× 2,199,315× 1,985,551× 2,319,993× 2,799,817× 2,515,663× 1,922,087× 1,431,256× 1,493,116× 1,728,830× 1,879,234× 1,916,671× 1,343,494× 941,934× 927,102× 795,521× 1,009,102× 932,267× 628,149× 411,500× 311,528× 237,766× 253,962× 234,312× 131,946× 40,008× 54,318× 108,323× 112,225× 52,254× 26,987× 10,942× 24,569× 57,208× 101,735× 60,865× 9,679× 2,354× 8,007× 538× | 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× 174,467× 714,674× 1,763,718× 3,338,018× 6,209,124× 8,439,022× 10,868,582× 12,258,170× 13,209,852× 13,066,868× 13,276,618× 16,568,058× 18,979,516× 18,663,320× 17,374,664× 15,184,394× 12,119,144× 10,848,716× 7,784,772× 7,332,322× 7,998,944× 7,320,154× 7,714,554× 6,781,948× 5,904,360× 5,677,858× 6,835,650× 8,149,606× 5,698,944× 2,521,704× 563,156× 82,584× 13,024× 2,374× | 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: 1× 3,086,187× 27,726,108× 43,597,263× 43,897,285× 38,546,614× 35,148,496× 43,118,511× 47,823,434× 57,030,330× 52,275,782× 53,283,585× 59,573,707× 64,361,498× 55,876,340× 47,962,861× 47,145,100× 55,357,113× 58,286,589× 50,885,535× 32,744,568× 24,055,455× 22,368,797× 24,676,660× 25,363,038× 19,360,133× 14,237,764× 11,821,284× 11,174,166× 9,068,661× 8,047,268× 5,953,643× 5,003,736× 3,551,526× 2,785,895× 3,114,109× 2,888,651× 1,895,469× 1,490,710× 1,072,448× 590,383× 813,139× 1,051,869× 1,566,974× 826,223× 334,923× 122,526× 57,051× 19,825× 11,567× 46,652× 1,956× | 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: 1× 1,512,343× 9,521,992× 25,261,296× 41,446,228× 64,549,450× 90,886,448× 118,623,684× 145,808,470× 165,823,908× 168,026,104× 146,749,954× 128,649,490× 119,801,614× 119,733,324× 117,863,376× 115,354,050× 129,954,512× 108,616,330× 80,884,336× 61,339,976× 47,278,126× 37,495,066× 31,517,508× 22,714,804× 20,776,524× 19,199,138× 23,443,598× 23,208,076× 22,562,574× 25,532,098× 27,906,818× 34,906,466× 46,443,650× 34,204,252× 24,694,478× 23,565,220× 24,710,684× 22,845,218× 14,574,282× 14,574,732× 17,841,932× 32,792,116× 53,599,624× 76,835,898× 125,457,494× 107,830,220× 115,738,688× 122,684,574× 149,083,500× 152,347,282× 141,338,170× 119,066,498× 103,690,164× 87,736,190× 70,376,086× 57,773,310× 50,839,286× 47,109,992× 37,319,606× 26,800,500× 20,936,800× 17,190,306× 13,731,582× 11,551,582× 8,930,912× 4,562,332× 2,461,360× 1,385,750× 820,246× 167,996× 1,182× |