| 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 Full Cycle | 1.97 step avg | 5.90 step avg | 8.89 step avg | 6.88 step avg | 10.74 step avg | 44.18 step avg | 20.80 step avg | 46.67 step avg | 18.94 step avg | 57.08 step avg | 41.78 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 30× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 30× 15× 30× 60× 120× 240× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 0× 1× 30× 511× 252× 502× 492× 478× 460× 438× 412× 382× 348× 310× 268× 222× 172× 118× 60× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 30× 0× 0× 0× 10,640× 30,905× 4,545× 255× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 0× 1× 30× 0× 3,867× 10,982× 12,314× 15,760× 26,743× 34,916× 48,314× 37,806× 42,966× 33,511× 26,457× 17,324× 9,324× 3,554× 763× | 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: 0× 1× 30× 0× 0× 0× 1,916× 5,269× 6,266× 3,364× 1,387× 2,299× 7,220× 1,681× 1,051× 193× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 12,732× 31,585× 56,220× 97,172× 139,762× 144,416× 172,129× 87,710× 76,187× 93,687× 144,924× 137,401× 91,020× 137,388× 73,882× 46,671× 49,713× 50,819× 36,978× 40,502× 17,104× 7,508× 13,602× 9,814× 16,444× 12,562× 18,752× 16,445× 22,511× 50,571× 7,910× 2,067× 578× 318× 31× | 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: 0× 1× 30× 0× 0× 0× 0× 0× 0× 38,572× 95,035× 195,390× 300,375× 392,443× 460,508× 543,485× 610,122× 829,312× 915,890× 959,963× 817,929× 742,876× 500,381× 323,335× 202,261× 205,041× 113,806× 120,149× 148,307× 179,163× 246,731× 244,528× 246,737× 229,509× 213,568× 163,387× 124,887× 72,219× 49,754× 9,778× | 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: 0× 1× 2,430× 17,988× 84,036× 42,892× 62,345× 68,708× 46,454× 11,940× 710× 0× 0× 0× 0× 0× 0× 0× 0× 18,758× 70,910× 225,162× 320,417× 701,471× 738,991× 681,338× 687,445× 1,070,671× 1,186,368× 964,869× 1,004,225× 1,278,612× 1,148,968× 1,127,922× 1,129,769× 1,282,527× 1,576,145× 1,498,417× 1,400,860× 1,255,651× 886,822× 959,424× 1,091,227× 1,397,763× 1,077,512× 849,848× 839,368× 1,153,205× 851,875× 887,875× 931,461× 1,296,599× 1,428,047× 1,257,345× 1,018,967× 1,210,293× 1,008,780× 960,395× 870,441× 528,951× 399,916× 438,812× 514,504× 482,155× 499,117× 452,050× 322,073× 270,770× 154,013× 118,245× 86,717× 135,627× 77,200× 58,456× 29,774× 97,599× 198,790× 298,324× 403,940× 268,346× 238,881× 294,996× 293,536× 130,363× 113,912× 246,393× 206,272× 203,377× 254,875× 248,254× 196,302× 209,709× 175,632× 94,628× 84,727× 68,553× 36,087× 38,809× 63,319× 147,954× 26,895× 10,392× | 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: 0× 1× 16,494× 129,068× 436,088× 810,616× 1,469,331× 2,253,910× 2,424,552× 2,425,138× 3,089,066× 3,600,100× 5,302,230× 8,497,809× 12,661,305× 16,337,894× 17,558,688× 17,104,969× 16,029,874× 15,496,007× 15,922,572× 15,365,028× 12,022,355× 8,562,098× 5,546,078× 3,513,502× 2,506,087× 2,195,781× 2,312,250× 2,773,346× 3,600,227× 2,512,911× 2,036,147× 1,022,164× 581,292× 533,915× 826,328× 1,037,111× 759,632× 583,587× 745,719× 754,276× 264,438× 244,720× 44,828× 5,600× | 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: 120s: 121s: 122s: 123s: 124s: 125s: 126s: 127s: 128s: 129s: 130s: 131s: 132s: 133s: 134s: 135s: 136s: 137s: 138s: 139s: 140s: 0× 1× 10,110× 131,240× 1,026,778× 2,819,960× 3,209,626× 4,115,394× 4,690,325× 6,180,789× 6,702,072× 7,675,978× 8,306,083× 6,575,514× 6,199,227× 7,098,227× 7,194,824× 6,580,904× 6,239,306× 6,632,977× 7,758,592× 4,380,191× 4,174,159× 2,774,936× 3,598,974× 4,901,264× 8,574,123× 7,679,625× 9,274,772× 9,443,755× 7,653,606× 8,072,459× 10,553,216× 12,712,924× 10,686,491× 6,548,529× 7,130,194× 7,480,533× 6,346,312× 7,054,741× 5,063,280× 2,985,023× 2,938,599× 4,581,622× 4,196,777× 5,155,257× 6,602,810× 7,176,143× 7,663,167× 8,590,684× 7,909,842× 7,759,925× 8,915,828× 12,191,222× 17,267,427× 18,945,710× 17,855,336× 16,396,888× 17,602,248× 18,988,919× 20,683,227× 16,827,093× 13,134,020× 13,087,372× 13,436,122× 15,375,030× 15,027,552× 13,713,263× 12,914,005× 10,565,786× 11,412,585× 8,783,753× 9,125,338× 9,878,176× 10,519,710× 9,990,690× 8,659,906× 6,338,015× 7,660,452× 9,754,937× 13,125,557× 10,189,002× 10,294,289× 7,332,280× 7,531,792× 6,719,158× 7,346,200× 6,710,136× 6,393,481× 6,231,145× 4,232,159× 2,885,362× 3,768,467× 4,736,383× 4,609,608× 7,348,494× 9,377,442× 6,314,160× 4,749,569× 2,798,696× 2,582,990× 3,571,648× 4,285,785× 2,503,625× 1,961,305× 2,634,979× 1,262,168× 1,340,718× 1,469,866× 2,126,534× 2,339,145× 2,127,387× 1,219,639× 1,000,519× 945,229× 410,956× 420,534× 587,004× 611,994× 528,819× 433,784× 197,536× 288,436× 178,000× 292,579× 543,922× 717,885× 1,673,016× 685,335× 350,532× 550,948× 534,390× 194,538× 140,933× 104,937× 57,811× 85,969× 8,329× 75,518× 34,524× 24,912× | 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: 0× 1× 30× 0× 0× 0× 0× 0× 268,848× 1,907,722× 6,356,860× 14,460,619× 21,755,746× 36,789,344× 57,162,102× 69,969,824× 68,084,271× 74,802,004× 80,314,751× 79,423,085× 67,761,675× 57,550,539× 45,093,025× 40,193,030× 38,915,979× 43,196,390× 43,416,519× 46,425,331× 57,674,021× 78,808,386× 81,003,481× 86,079,593× 76,815,101× 67,046,392× 56,617,143× 50,110,243× 42,949,441× 41,377,321× 43,864,917× 45,016,154× 60,161,349× 77,787,069× 98,505,370× 73,986,050× 53,449,566× 43,050,682× 39,525,905× 31,552,914× 23,929,446× 16,672,921× 11,912,700× 13,476,746× 24,083,009× 32,905,272× 45,010,109× 38,301,154× 39,946,352× 37,415,214× 32,565,319× 33,542,923× 30,598,457× 21,957,042× 20,813,309× 18,571,368× 18,846,390× 24,599,077× 25,819,450× 32,505,247× 30,366,332× 25,354,347× 25,188,755× 26,931,870× 24,863,955× 28,148,348× 30,050,180× 31,547,444× 35,454,565× 45,955,244× 48,347,008× 43,476,910× 31,867,666× 23,172,512× 21,468,985× 17,109,145× 15,829,842× 8,074,850× 3,034,006× 493,838× 25,868× |