| 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 | 5.96 step avg | 8.59 step avg | 10.62 step avg | 12.07 step avg | 24.60 step avg | 24.29 step avg | 24.07 step avg | 17.97 step avg | 21.53 step avg | 35.37 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 31× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 2× 51× 10× 0× 7× 228× 230× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 0× 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: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 0× 1× 31× 0× 0× 0× 672× 1,913× 5,421× 8,750× 8,152× 9,298× 8,492× 4,046× 5,584× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 0× 1× 31× 782× 272× 5,764× 9,276× 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: 38s: 39s: 40s: 41s: 42s: 43s: 44s: 45s: 46s: 47s: 48s: 49s: 50s: 51s: 52s: 53s: 0× 1× 303× 0× 1,452× 3,396× 20,856× 51,704× 47,262× 42,814× 30,815× 37,576× 40,977× 38,752× 63,504× 49,956× 78,101× 90,011× 94,608× 111,723× 87,474× 74,933× 75,553× 81,431× 73,185× 79,146× 103,422× 106,285× 92,316× 101,958× 75,966× 46,252× 41,454× 29,639× 29,678× 44,640× 32,617× 45,705× 25,790× 36,496× 33,094× 48,356× 35,048× 14,830× 14,630× 15,634× 18,232× 11,026× 13,336× 15,018× 9,262× 2,487× 3,964× 2,116× | 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: 0× 1× 5,863× 21,916× 52,548× 81,160× 116,754× 180,708× 341,570× 415,986× 357,538× 132,252× 70,352× 37,486× 19,724× 0× 0× 0× 0× 0× 105,416× 242,988× 466,640× 694,854× 975,366× 1,035,662× 1,155,808× 1,225,602× 1,441,778× 1,281,138× 971,854× 527,710× 293,400× 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: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 62s: 63s: 64s: 0× 1× 31× 0× 0× 0× 180,006× 912,913× 1,006,956× 842,705× 774,085× 903,905× 1,805,245× 2,062,019× 1,727,592× 1,605,480× 1,740,450× 2,284,479× 2,731,794× 2,894,392× 2,351,342× 2,017,098× 2,259,927× 2,851,383× 3,223,258× 2,850,969× 2,063,271× 1,643,781× 1,933,120× 2,431,323× 2,411,604× 2,048,820× 1,276,543× 976,463× 1,019,184× 1,150,513× 1,169,665× 914,779× 620,602× 472,021× 496,329× 790,855× 759,670× 508,318× 346,589× 198,889× 150,709× 227,098× 213,329× 109,951× 25,636× 29,441× 67,530× 92,209× 47,104× 26,475× 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: 35s: 36s: 0× 1× 18,825× 118,584× 372,208× 785,080× 1,686,444× 3,338,898× 4,984,914× 6,696,924× 9,728,640× 11,789,190× 14,282,452× 15,176,656× 19,359,446× 20,806,358× 20,362,496× 18,141,892× 16,349,954× 13,796,140× 12,402,628× 9,289,106× 8,392,062× 8,288,706× 7,325,514× 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: 52s: 53s: 54s: 55s: 56s: 57s: 58s: 59s: 60s: 61s: 0× 1× 31× 15,600× 122,332× 201,827× 1,040,937× 8,784,626× 13,076,705× 16,224,653× 16,235,136× 17,523,508× 39,940,225× 52,361,821× 52,345,308× 47,845,924× 49,098,076× 56,152,371× 63,578,197× 61,109,296× 51,040,834× 49,897,105× 55,832,376× 59,665,648× 57,556,999× 44,187,512× 35,812,111× 36,629,190× 37,519,815× 34,880,523× 25,486,973× 18,957,387× 18,738,028× 19,398,251× 16,142,083× 11,082,484× 8,772,577× 7,356,553× 6,886,153× 5,627,715× 4,434,028× 2,936,559× 1,941,100× 1,630,194× 1,623,502× 2,047,860× 2,137,729× 1,737,031× 1,285,949× 878,579× 464,636× 549,579× 721,643× 939,215× 354,740× 185,696× 61,636× 25,338× 4,870× 5,635× 5,042× 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: 72s: 73s: 74s: 75s: 0× 1× 31× 0× 0× 384,000× 3,069,440× 9,780,102× 21,237,566× 37,411,444× 60,007,292× 82,204,166× 100,559,624× 110,735,732× 90,954,794× 95,382,472× 92,304,262× 109,196,832× 113,658,332× 132,788,504× 134,523,254× 156,753,184× 186,461,820× 162,115,388× 115,748,392× 87,152,496× 64,579,900× 51,808,978× 39,929,404× 30,328,922× 27,604,896× 25,902,864× 25,833,538× 26,729,790× 28,733,668× 32,923,270× 36,604,204× 46,908,190× 35,475,234× 25,958,384× 24,002,472× 24,808,240× 22,850,102× 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× |