| 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 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.96 step avg | 5.55 step avg | 8.12 step avg | 10.49 step avg | 10.44 step avg | 40.39 step avg | 19.73 step avg | 34.21 step avg | 19.48 step avg | 44.78 step avg | 59.20 step avg | 27.62 step avg | 68.28 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 26× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 26× 15× 69× 33× 78× 156× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 26× 391× 192× 382× 372× 358× 340× 318× 292× 262× 228× 190× 148× 102× 52× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 0× 1× 26× 0× 600× 1,242× 0× 0× 0× 0× 5,588× 16,672× 3,081× 195× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 0× 1× 926× 1,759× 2,546× 5,626× 12,034× 15,833× 13,551× 15,150× 14,692× 16,171× 19,436× 19,082× 14,569× 10,025× 5,689× 1,953× 816× 52× | 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: 0× 1× 602× 976× 4,496× 23,478× 7,760× 8,601× 7,886× 7,937× 14,979× 15,979× 19,938× 45,191× 48,464× 44,105× 19,166× 26,046× 19,646× 12,944× 15,472× 19,811× 10,516× 3,079× 3,524× 6,797× 9,982× 14,968× 9,835× 5,049× 2,923× 3,127× 1,299× 591× 50× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 19,382× 42,721× 68,052× 121,319× 55,332× 43,750× 31,507× 22,718× 20,729× 14,553× 10,803× 7,169× 4,555× 6,760× 1,152× 472× | 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: 0× 1× 26× 0× 0× 0× 0× 0× 0× 22,832× 48,984× 96,295× 120,987× 144,673× 225,060× 293,747× 346,610× 422,938× 509,758× 430,688× 312,210× 238,505× 154,895× 92,608× 50,155× 40,795× 31,900× 40,663× 47,699× 76,854× 102,909× 93,637× 94,670× 76,569× 46,935× 40,229× 36,280× 20,688× 11,248× | 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: 0× 1× 3,406× 18,094× 69,736× 47,136× 62,193× 55,409× 100,369× 88,572× 141,776× 149,025× 104,234× 101,952× 74,310× 144,035× 235,514× 210,699× 287,566× 105,877× 106,907× 98,963× 103,882× 147,741× 242,641× 316,841× 477,740× 656,847× 729,827× 886,055× 807,178× 857,891× 688,324× 475,021× 511,320× 569,618× 506,617× 625,958× 616,759× 627,712× 448,731× 689,210× 639,672× 619,115× 540,895× 550,336× 419,283× 454,455× 388,840× 292,951× 155,297× 112,817× 98,711× 64,864× 85,885× 132,720× 149,094× 77,917× 70,821× 30,216× 17,115× 10,757× 18,700× 10,561× 18,558× 3,563× 1,262× 112× | 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: 0× 1× 8,666× 54,015× 145,211× 201,673× 372,092× 602,206× 1,008,031× 1,607,654× 2,473,513× 2,711,065× 3,040,261× 3,193,978× 3,207,386× 3,229,255× 3,498,139× 4,388,918× 5,033,270× 4,730,883× 4,254,879× 3,711,276× 2,968,668× 2,201,892× 1,815,151× 1,712,706× 1,756,382× 1,810,689× 1,554,591× 1,645,429× 1,384,971× 1,127,841× 902,286× 694,919× 803,714× 733,252× 831,230× 551,381× 393,999× 143,820× 74,897× 19,767× 5,739× 1,764× | 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: 0× 1× 926× 1,620× 1,321× 0× 0× 21,536× 222,338× 1,991,773× 2,835,186× 2,840,159× 1,757,372× 1,650,278× 2,010,634× 2,561,669× 3,083,529× 3,864,137× 3,427,693× 2,756,380× 1,918,433× 1,766,276× 1,921,352× 2,319,001× 2,893,541× 2,095,724× 2,110,475× 1,267,160× 1,164,013× 1,061,773× 1,757,280× 2,545,503× 2,796,350× 3,079,806× 3,350,755× 3,891,645× 3,565,970× 4,513,823× 6,022,085× 8,360,803× 8,051,831× 6,137,183× 6,018,959× 5,408,112× 5,621,268× 5,321,602× 4,689,057× 4,287,605× 3,283,813× 3,501,347× 4,551,102× 6,297,166× 5,442,288× 5,582,207× 5,946,093× 6,868,236× 7,591,938× 6,489,010× 5,691,385× 4,801,961× 5,185,230× 5,649,620× 7,261,552× 6,940,446× 5,574,120× 5,440,910× 4,004,460× 4,326,401× 2,715,239× 2,722,975× 1,618,825× 1,030,518× 568,903× 590,499× 361,028× 478,835× 235,235× 89,810× 126,139× 41,776× 31,308× 74,785× 31,294× 22,206× 9,154× 10,638× 9,605× 9,212× 13,298× 2,352× | 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: 0× 1× 1,646× 2,700× 0× 0× 0× 0× 0× 141,008× 749,947× 1,855,712× 2,375,389× 3,054,777× 2,765,684× 3,054,073× 2,924,305× 4,989,431× 6,518,381× 8,496,996× 11,195,100× 15,212,469× 14,578,001× 14,993,308× 14,728,984× 10,845,569× 6,288,457× 4,444,101× 4,632,028× 2,956,035× 2,542,274× 2,445,362× 3,083,789× 4,212,573× 5,854,353× 6,727,465× 8,681,764× 7,436,494× 7,457,502× 7,738,939× 9,136,860× 6,408,310× 6,589,761× 6,556,217× 7,515,955× 8,846,813× 11,637,533× 10,952,398× 10,086,828× 8,968,189× 7,351,047× 5,887,929× 5,608,957× 5,933,644× 3,712,895× 4,231,419× 4,172,148× 3,813,716× 4,803,207× 3,987,230× 4,360,238× 8,165,384× 14,359,429× 17,882,094× 21,026,845× 23,223,889× 23,032,448× 21,153,569× 19,915,027× 18,810,864× 18,393,130× 20,307,411× 28,179,563× 25,030,636× 20,531,896× 16,805,991× 15,903,669× 19,048,256× 19,800,448× 23,411,287× 19,026,007× 15,161,995× 14,328,729× 14,882,510× 12,868,323× 10,410,483× 9,098,733× 9,480,540× 7,357,376× 6,098,745× 7,172,020× 5,206,394× 5,083,017× 3,627,195× 3,992,097× 1,654,256× 623,971× 174,560× 168,300× 49,154× | 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: 0× 1× 26× 0× 56,064× 515,068× 4,431,463× 10,021,994× 16,426,542× 36,071,699× 65,230,222× 73,995,395× 76,005,814× 72,371,911× 81,599,765× 79,444,329× 89,115,186× 93,113,222× 101,394,732× 89,199,831× 79,825,545× 88,964,746× 94,171,006× 98,063,832× 106,219,148× 86,405,378× 82,976,999× 70,743,127× 61,729,701× 57,172,978× 58,036,678× 59,535,019× 43,832,671× 42,838,159× 44,987,795× 46,157,862× 45,082,619× 41,260,484× 34,904,392× 30,523,515× 33,469,474× 37,631,012× 35,790,973× 37,742,287× 40,255,179× 41,590,847× 38,773,453× 38,376,924× 31,948,780× 24,348,584× 15,974,160× 14,430,584× 11,914,868× 14,123,500× 13,540,206× 12,904,382× 11,161,081× 10,201,769× 5,675,966× 5,963,162× 6,014,358× 5,708,265× 6,560,843× 2,927,821× 3,220,584× 3,054,865× 2,582,800× 5,059,391× 3,543,995× 3,710,724× 3,426,987× 3,895,738× 5,631,409× 3,528,300× 4,102,130× 2,996,716× 1,939,010× 803,148× 395,834× 117,986× 12,135× | 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: 141s: 142s: 143s: 144s: 145s: 146s: 0× 1× 1,646× 2,520× 0× 302,320× 3,248,380× 12,475,120× 19,023,145× 29,554,844× 40,662,317× 45,124,484× 41,457,048× 35,296,253× 33,240,267× 30,152,585× 26,583,309× 24,573,078× 36,118,119× 31,666,283× 31,635,514× 31,363,973× 31,731,530× 36,628,575× 36,062,922× 28,314,419× 25,849,272× 18,990,800× 15,321,975× 8,999,490× 6,802,647× 4,585,107× 1,786,037× 898,883× 55,088× 0× 0× 0× 0× 0× 0× 0× 1,637,448× 16,122,276× 47,534,103× 75,725,590× 121,865,304× 167,267,291× 199,369,891× 203,742,730× 213,545,889× 176,391,049× 164,977,369× 164,882,507× 148,952,872× 140,167,397× 121,587,140× 116,466,690× 125,669,002× 133,510,398× 123,831,004× 99,235,954× 104,434,998× 111,588,507× 113,848,236× 134,031,928× 140,066,241× 137,847,952× 136,070,107× 135,738,577× 124,218,618× 141,217,593× 158,166,695× 182,722,286× 190,346,114× 176,537,824× 144,243,841× 129,626,170× 111,953,773× 84,664,388× 83,989,518× 89,068,908× 90,552,952× 78,908,817× 69,292,685× 75,054,896× 72,356,911× 65,975,314× 67,890,464× 74,724,781× 88,957,197× 92,480,499× 92,947,749× 89,812,086× 109,603,261× 91,277,941× 76,081,060× 60,064,879× 51,477,232× 49,620,264× 59,228,265× 43,991,547× 45,612,158× 41,725,225× 31,923,320× 31,587,107× 28,004,687× 23,009,292× 23,264,782× 29,699,149× 28,076,522× 35,636,186× 58,851,143× 64,330,166× 49,787,557× 42,958,701× 33,663,277× 20,454,878× 11,512,939× 9,450,122× 8,116,555× 6,826,452× 6,761,883× 5,393,751× 4,333,856× 3,627,374× 3,103,536× 4,206,959× 3,821,813× 6,054,254× 7,354,017× 10,006,399× 8,259,740× 10,312,049× 9,577,663× 9,717,018× 7,024,818× 2,356,412× 2,499,803× 3,177,191× 3,734,493× 2,506,104× 1,326,516× 819,943× 161,005× 81,612× 46,088× |