| 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 | 14 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.96 step avg | 1.42 step avg | 6.06 step avg | 4.23 step avg | 8.80 step avg | 19.16 step avg | 6.51 step avg | 39.54 step avg | 11.11 step avg | 28.11 step avg | 20.51 step avg | 31.66 step avg | 15.56 step avg | 41.26 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 23× | 0s: 1s: 2s: 7× 161× 132× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 1× 179× 154× 306× 298× 286× 270× 250× 226× 198× 166× 130× 90× 46× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 980× 1,439× 3,364× 5,352× 2,852× 1,672× 1,068× 360× 462× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 1× 1,113× 1,472× 1,862× 3,536× 6,670× 11,600× 10,372× 8,658× 9,220× 9,580× 11,666× 9,796× 7,668× 3,812× 1,208× 46× | 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: 1× 14,207× 27,238× 27,562× 22,098× 24,327× 23,592× 21,537× 17,670× 17,728× 13,951× 14,057× 15,278× 15,117× 9,695× 4,260× 2,196× 5,024× 7,464× 2,831× 2,960× 2,258× 2,247× 1,706× 2,512× 1,492× 3,558× 2,774× 3,874× 6,708× 4,741× 7,375× 10,865× 10,132× 8,174× 7,790× 10,202× 8,483× 13,546× 13,186× 5,533× 5,752× 7,261× 6,738× 7,896× 7,104× 4,494× 7,498× 4,538× 2,392× 3,092× 758× 1,362× 186× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 1× 38,027× 78,186× 127,298× 162,798× 241,892× 326,420× 359,792× 307,706× 209,326× 97,368× 47,036× 22,626× 13,904× 3,420× | 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: 1× 33,519× 121,646× 122,365× 134,907× 159,615× 161,095× 168,618× 136,953× 118,117× 160,663× 145,433× 136,171× 148,105× 163,848× 154,895× 140,215× 148,786× 150,528× 139,257× 149,143× 170,007× 183,058× 156,944× 152,074× 106,856× 115,037× 96,317× 92,853× 70,763× 82,631× 107,162× 87,789× 67,433× 57,052× 67,290× 67,781× 91,773× 57,116× 29,241× 27,263× 46,553× 50,779× 55,045× 66,540× 51,997× 55,580× 44,571× 46,660× 69,102× 73,328× 89,521× 98,432× 104,206× 97,069× 77,245× 60,479× 43,301× 51,959× 57,295× 48,560× 35,370× 40,376× 46,937× 31,668× 17,145× 25,112× 42,018× 36,560× 43,949× 38,961× 25,969× 12,491× 7,074× 19,464× 35,429× 32,795× 29,102× 28,624× 44,459× 58,308× 41,937× 45,754× 56,877× 73,433× 46,450× 51,102× 56,381× 58,900× 89,248× 79,482× 93,387× 72,895× 68,338× 46,197× 27,097× 25,408× 23,451× 29,378× 50,257× 46,181× 27,298× 29,171× 34,158× 42,459× 25,737× 15,728× 8,252× 3,416× | 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× 162,767× 569,034× 940,170× 1,294,706× 1,901,740× 2,281,564× 2,125,056× 2,107,430× 1,688,232× 1,350,772× 1,294,302× 1,407,438× 1,729,500× 1,761,138× 1,658,690× 1,191,440× 808,756× 595,050× 648,506× 482,586× 471,728× 203,496× 169,620× 299,986× 348,752× 199,166× 73,178× 51,686× 64,026× 58,466× 40,712× 50,524× 18,582× | 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: 89s: 1× 194,948× 1,497,060× 2,290,426× 2,101,056× 2,150,893× 1,915,123× 1,879,914× 2,094,938× 1,984,803× 1,851,381× 1,760,214× 1,571,927× 1,665,972× 1,816,342× 2,097,890× 2,242,286× 1,949,093× 2,028,111× 1,698,236× 1,552,563× 1,526,806× 1,632,219× 1,552,948× 1,735,537× 1,649,093× 1,664,190× 1,647,619× 1,917,543× 2,098,159× 2,314,245× 2,168,176× 1,814,383× 1,569,693× 1,555,400× 1,446,358× 1,734,495× 1,532,233× 1,426,547× 1,343,864× 1,543,330× 1,585,650× 1,697,966× 1,491,332× 1,138,425× 902,533× 1,067,400× 991,325× 767,509× 520,278× 650,728× 651,387× 637,758× 727,066× 716,016× 712,327× 686,779× 695,616× 656,322× 540,444× 486,030× 406,042× 433,193× 347,715× 564,487× 580,265× 369,412× 217,858× 200,194× 156,024× 140,918× 197,500× 298,687× 282,248× 162,783× 118,138× 64,257× 76,023× 89,378× 83,307× 90,883× 74,508× 43,172× 18,514× 1,316× 844× 1,664× 1,184× 528× 1,092× | 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: 1× 285,295× 1,610,920× 4,166,522× 5,288,118× 6,799,754× 7,859,330× 8,517,502× 7,061,440× 6,904,428× 8,344,394× 10,609,764× 11,631,200× 8,362,036× 6,399,890× 7,610,660× 9,138,104× 11,761,552× 11,228,688× 8,966,218× 9,212,770× 9,325,852× 9,532,280× 7,067,624× 5,754,532× 4,768,784× 4,468,990× 4,431,662× 5,184,160× 6,959,322× 9,495,170× 9,497,608× 9,777,680× 9,589,554× 9,552,438× 8,268,120× 5,593,346× 4,183,034× 3,261,032× 2,886,888× 2,344,472× 1,442,824× 689,470× 163,238× 86,616× 14,478× | 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: 1× 374,567× 6,519,766× 13,426,810× 13,035,263× 12,606,713× 13,613,666× 16,329,847× 18,233,231× 16,986,360× 17,592,717× 16,868,884× 17,161,257× 15,178,056× 13,942,586× 13,964,354× 14,249,402× 13,519,894× 14,413,894× 16,041,370× 15,690,587× 15,788,030× 14,607,421× 13,688,201× 12,433,130× 11,317,804× 12,435,469× 15,203,651× 15,914,407× 16,005,624× 15,488,256× 15,524,782× 17,208,895× 18,244,916× 17,212,173× 16,812,445× 17,287,229× 17,943,637× 17,179,049× 14,193,380× 11,902,808× 9,987,612× 10,171,819× 12,488,206× 12,739,598× 12,672,302× 11,780,992× 12,302,885× 9,537,261× 10,057,363× 10,342,601× 10,425,207× 9,598,324× 7,881,149× 6,397,735× 5,731,226× 5,684,505× 6,535,853× 6,019,332× 4,871,157× 4,894,441× 4,987,515× 4,480,823× 3,648,430× 4,139,864× 4,517,194× 3,524,894× 2,965,919× 2,605,676× 2,873,396× 3,209,743× 2,082,437× 1,643,415× 1,452,303× 1,163,840× 950,313× 929,566× 1,638,616× 1,491,861× 1,641,326× 1,679,722× 1,280,372× 841,940× 625,170× 572,880× 534,413× 873,687× 684,135× 639,296× 1,072,378× 1,301,397× 1,818,329× 1,668,280× 1,149,199× 873,048× 604,821× 487,972× 328,152× 394,520× 126,945× 151,224× 182,632× 80,722× 132,190× 18,910× 17,108× 39,318× 26,296× 21,989× 13,173× 4,351× | 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× 854,631× 8,571,712× 23,471,140× 40,541,186× 66,132,974× 95,107,928× 123,028,668× 142,962,748× 160,724,456× 159,734,498× 131,148,886× 96,750,324× 83,269,896× 76,145,926× 75,645,546× 68,752,486× 77,850,222× 87,499,954× 94,941,614× 89,126,202× 82,015,476× 73,438,790× 58,290,650× 51,406,062× 49,856,812× 50,082,268× 41,348,170× 32,297,130× 22,904,318× 18,754,440× 18,176,996× 22,638,930× 15,844,072× 12,230,914× 9,711,720× 6,497,430× 4,362,448× 5,448,966× 4,795,590× 4,460,246× 5,115,886× 5,155,930× 4,291,142× 3,128,848× 2,745,358× 1,700,106× 1,436,198× 377,032× 16,674× | 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: 147s: 148s: 149s: 1× 613,377× 22,788,122× 49,407,521× 40,622,226× 46,075,852× 64,117,827× 97,411,814× 124,525,474× 123,079,893× 109,581,312× 93,367,894× 82,624,818× 68,775,957× 65,623,421× 66,296,999× 70,095,191× 93,210,116× 110,388,213× 130,264,362× 135,253,535× 119,352,400× 120,747,584× 116,509,862× 113,855,581× 102,295,226× 90,836,135× 85,969,217× 91,467,541× 95,275,894× 104,441,688× 103,085,198× 110,167,184× 116,232,696× 115,373,688× 99,897,780× 90,142,465× 84,724,568× 75,653,957× 71,775,442× 75,072,556× 72,924,235× 76,293,954× 75,779,636× 70,791,034× 69,673,434× 67,357,164× 67,447,823× 59,439,797× 53,340,228× 52,895,740× 49,915,643× 53,989,311× 54,824,595× 51,978,154× 60,910,365× 53,393,731× 48,258,490× 38,541,339× 38,601,455× 45,311,276× 47,573,502× 47,533,326× 53,211,319× 46,989,818× 48,339,956× 43,787,582× 35,689,271× 32,162,102× 25,844,780× 24,505,665× 23,099,259× 21,892,295× 25,944,993× 33,754,753× 40,322,349× 35,656,754× 37,056,854× 33,522,445× 29,144,687× 28,857,357× 27,670,152× 24,896,646× 20,478,556× 16,622,237× 16,565,555× 15,728,870× 18,730,669× 22,003,862× 18,775,797× 18,608,883× 15,046,167× 13,366,594× 15,914,701× 17,619,493× 15,200,439× 12,323,497× 13,009,351× 18,030,716× 22,579,735× 22,918,633× 22,205,449× 16,626,781× 13,521,410× 12,723,226× 9,584,973× 8,545,001× 8,487,866× 8,266,122× 10,087,157× 13,150,880× 10,567,850× 10,886,284× 10,965,476× 11,563,468× 8,814,144× 8,068,609× 5,540,190× 3,433,842× 2,616,091× 1,882,340× 2,193,039× 3,196,254× 6,093,019× 6,758,136× 11,011,904× 11,201,169× 7,851,942× 6,363,563× 6,454,591× 5,374,094× 3,270,360× 2,805,726× 2,305,746× 2,256,590× 1,935,643× 2,309,533× 3,550,544× 1,664,852× 838,525× 596,794× 302,576× 423,085× 150,093× 296,652× 525,612× 145,220× 4,904× 13,654× 8,210× |