| 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 | 4.90 step avg | 6.89 step avg | 1.88 step avg | 7.41 step avg | 11.62 step avg | 12.80 step avg | 27.44 step avg | 11.63 step avg | 53.25 step avg | 33.64 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 30× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 1× 30× 15× 30× 60× 120× 240× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 1× 541× 252× 502× 492× 478× 460× 438× 412× 382× 348× 310× 268× 222× 172× 118× 60× | 0s: 1s: 2s: 3s: 4s: 1× 10,670× 30,905× 4,545× 255× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 1× 9,124× 13,011× 10,452× 22,616× 31,804× 40,434× 37,365× 38,326× 39,670× 27,528× 23,605× 17,115× 9,264× 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: 1× 14,678× 36,854× 62,486× 100,536× 141,149× 146,715× 179,349× 89,391× 77,238× 93,880× 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: 1× 38,602× 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: 1× 51,509× 214,275× 756,096× 678,880× 673,125× 796,609× 972,730× 964,305× 1,031,148× 1,163,212× 1,149,693× 1,020,373× 1,174,830× 1,198,294× 1,237,451× 1,228,885× 1,110,345× 1,340,901× 1,618,554× 1,284,296× 963,752× 774,214× 1,119,373× 1,226,586× 1,250,545× 962,826× 1,212,649× 1,053,951× 978,001× 834,579× 1,024,938× 1,366,295× 1,493,882× 1,244,018× 1,117,617× 971,400× 1,219,861× 1,040,658× 619,999× 436,737× 454,994× 519,956× 492,946× 502,413× 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: 1× 439,421× 1,765,236× 4,014,763× 6,802,071× 11,131,893× 14,734,296× 16,770,804× 16,780,465× 17,343,488× 16,315,508× 14,892,461× 13,306,335× 12,280,489× 11,591,601× 11,094,638× 9,660,384× 7,103,182× 5,187,430× 3,230,898× 2,091,350× 1,101,438× 922,625× 1,001,758× 2,042,793× 1,409,613× 1,592,992× 925,753× 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: 1× 50,022× 528,728× 4,620,079× 6,670,857× 6,267,550× 5,371,101× 7,177,159× 7,076,020× 6,255,763× 6,130,232× 7,623,967× 8,825,772× 8,041,595× 6,655,668× 6,265,561× 5,798,379× 5,503,628× 5,597,984× 3,781,527× 4,141,492× 5,171,901× 8,342,036× 7,631,515× 9,697,012× 9,772,743× 7,896,481× 7,492,681× 9,198,146× 10,724,041× 9,864,878× 8,253,247× 7,975,467× 7,709,075× 7,579,064× 7,231,427× 4,647,622× 3,027,119× 3,427,761× 5,269,313× 4,569,531× 5,194,840× 6,625,810× 7,202,109× 7,664,505× 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: 1× 1,668,549× 8,907,843× 20,563,295× 32,658,912× 50,290,994× 77,608,244× 90,565,324× 82,340,184× 66,450,640× 65,278,474× 53,987,028× 42,566,488× 43,118,865× 44,468,863× 40,252,718× 39,977,787× 42,185,049× 43,218,212× 45,703,623× 55,310,947× 77,130,221× 79,570,067× 89,691,219× 77,300,977× 68,625,281× 56,463,286× 51,764,840× 43,125,349× 41,533,238× 43,867,216× 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× |