| 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 |
|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.98 step avg | 2.17 step avg | 9.55 step avg | 1.83 step avg | 12.42 step avg | 33.99 step avg | 14.26 step avg | 36.68 step avg | 16.39 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 44× | 0s: 1s: 2s: 3s: 7× 291× 253× 484× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 1× 1,101× 525× 1,048× 1,038× 1,024× 1,006× 984× 958× 928× 894× 856× 814× 768× 718× 664× 606× 544× 478× 408× 334× 256× 174× 88× | 0s: 1s: 2s: 3s: 4s: 1× 46,090× 135,355× 12,606× 528× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 1× 3,884× 6,349× 10,010× 22,282× 36,060× 63,640× 85,505× 110,136× 124,021× 171,540× 155,772× 181,572× 175,246× 167,543× 143,135× 131,574× 94,458× 84,001× 65,524× 43,314× 22,306× 7,429× 1,582× | 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: 1× 101,860× 284,140× 517,839× 361,845× 314,681× 376,750× 305,052× 266,310× 240,390× 265,480× 244,677× 239,840× 234,547× 238,677× 250,341× 310,198× 289,517× 280,783× 295,898× 221,558× 245,506× 207,278× 266,684× 292,591× 302,271× 323,685× 291,424× 319,586× 280,522× 189,131× 168,763× 133,885× 145,269× 129,545× 115,005× 122,498× 99,961× 118,331× 102,721× 136,970× 127,116× 151,032× 164,033× 169,865× 189,730× 168,121× 213,223× 169,726× 253,564× 234,760× 223,800× 235,270× 213,588× 244,758× 127,513× 109,263× 113,269× 167,177× 206,615× 209,634× 139,738× 124,637× 135,812× 122,185× 187,284× 153,534× 161,824× 122,704× 81,718× 85,516× 83,087× 141,905× 153,955× 157,089× 80,022× 75,305× 66,069× 78,136× 71,405× 68,088× 71,421× 67,759× 52,845× 16,374× 30,736× 28,294× 3,479× 5,712× | 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: 1× 161,744× 365,848× 873,665× 1,527,305× 2,473,511× 3,288,251× 4,843,521× 6,318,484× 7,219,587× 7,825,123× 8,532,136× 7,919,842× 8,222,809× 6,811,126× 6,223,753× 4,896,820× 4,221,600× 3,520,392× 4,180,742× 3,939,339× 4,488,762× 4,312,819× 4,157,596× 3,539,007× 2,237,857× 1,500,296× 926,260× 672,747× 295,314× 214,844× 49,497× 7,701× 6,801× | 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: 115s: 116s: 117s: 118s: 119s: 1× 492,445× 2,189,586× 10,555,535× 17,054,775× 16,998,293× 17,063,763× 17,981,820× 18,141,031× 20,157,915× 22,582,969× 23,246,138× 20,736,561× 19,846,949× 18,614,329× 18,831,001× 18,223,059× 13,160,298× 12,919,709× 15,340,046× 15,382,586× 11,552,048× 8,807,472× 8,787,330× 8,089,359× 8,178,061× 8,675,446× 7,110,050× 5,720,817× 5,188,467× 7,153,477× 5,187,050× 4,851,908× 4,606,941× 5,169,491× 5,666,663× 5,558,750× 4,672,723× 4,529,964× 4,213,169× 5,454,332× 6,534,854× 7,209,727× 7,069,867× 7,785,139× 9,880,228× 8,072,565× 8,788,142× 7,862,424× 8,788,278× 9,829,101× 6,533,119× 6,640,579× 8,482,460× 7,399,979× 7,410,274× 6,474,046× 5,954,603× 5,809,939× 5,043,269× 3,961,640× 2,626,643× 2,494,354× 3,778,677× 3,902,426× 2,539,507× 2,454,469× 2,484,159× 2,481,678× 3,702,989× 2,891,623× 3,283,626× 2,694,271× 3,491,364× 4,747,632× 6,649,663× 7,315,826× 6,851,300× 6,617,641× 6,054,724× 4,514,718× 3,837,599× 4,795,170× 4,290,816× 4,285,276× 3,452,025× 3,221,471× 2,619,735× 2,590,726× 3,067,368× 2,406,570× 2,990,183× 4,209,016× 3,809,888× 3,730,681× 2,220,756× 3,095,487× 3,102,736× 2,537,514× 2,340,309× 1,469,837× 1,667,762× 1,438,796× 892,939× 614,368× 1,356,071× 942,608× 774,521× 1,141,069× 1,124,974× 704,345× 751,521× 664,401× 226,588× 115,879× 154,344× 12,791× 22,384× 58,708× 1,068× | 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× 2,459,101× 12,386,463× 30,052,248× 55,923,411× 100,616,897× 133,860,033× 177,718,306× 191,517,521× 204,438,880× 213,667,329× 222,886,282× 235,608,228× 258,139,880× 282,560,346× 266,226,918× 254,912,221× 206,840,828× 173,478,144× 131,144,095× 115,880,743× 104,894,630× 103,687,703× 92,706,316× 95,065,473× 88,100,235× 69,949,782× 66,560,265× 63,593,568× 75,167,265× 69,318,918× 62,587,761× 58,864,258× 58,876,758× 41,841,906× 26,453,815× 21,734,231× 15,602,378× 11,709,162× 9,766,315× 7,339,248× 3,303,218× 1,995,517× 1,757,205× 3,610,543× 3,786,110× 1,673,275× 934,366× 340,354× 75,100× |