| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.97 step avg | 6.17 step avg | 8.21 step avg | 6.82 step avg | 10.86 step avg | 56.75 step avg | 16.54 step avg | 56.36 step avg | 16.08 step avg | 112.11 step avg | 44.29 step avg | 97.87 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 29× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 29× 0× 0× 8× 217× 210× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 0× 1× 269× 238× 474× 466× 454× 438× 418× 394× 366× 334× 298× 258× 214× 166× 114× 58× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 0× 1× 185× 674× 2,076× 5,736× 4,927× 17,056× 4,479× 3,891× 1,143× 752× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 0× 1× 1,239× 2,972× 3,610× 7,482× 14,552× 21,366× 22,268× 24,416× 23,914× 28,896× 34,308× 27,640× 22,334× 19,774× 15,156× 6,756× 1,572× | 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: 0× 1× 269× 0× 0× 0× 11,432× 29,976× 18,420× 9,266× 12,529× 13,145× 15,410× 13,918× 4,110× 9,051× 14,193× 24,985× 26,961× 14,973× 21,238× 28,091× 16,715× 17,102× 19,780× 27,565× 21,710× 15,243× 7,256× 2,616× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 16,169× 40,394× 36,807× 32,778× 37,898× 37,246× 42,690× 50,074× 54,208× 51,406× 38,276× 28,978× 29,907× 30,598× 22,193× 24,280× 19,045× 14,963× 15,722× 12,756× 21,093× 16,183× 18,973× 20,103× 30,363× 25,219× 28,433× 30,803× 22,851× 19,991× 15,512× 11,873× 11,167× 15,736× 14,698× 12,796× 10,774× 8,083× 10,549× 12,612× 17,124× 17,115× 22,340× 18,148× 10,974× 11,610× 13,790× 16,380× 8,992× 11,957× 11,663× 17,425× 21,070× 15,594× 7,052× 6,614× 3,802× 1,355× | 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: 0× 1× 29× 0× 0× 17,480× 41,294× 72,922× 98,992× 173,234× 169,978× 269,264× 326,456× 459,164× 540,102× 597,250× 778,736× 973,644× 1,151,094× 985,404× 754,212× 540,198× 265,112× 93,918× 34,788× 4,408× | 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: 0× 1× 2,229× 6,074× 5,376× 16,082× 11,711× 4,230× 0× 0× 0× 31,056× 196,942× 267,272× 258,500× 388,704× 577,106× 695,929× 667,593× 580,714× 573,537× 794,608× 763,227× 787,497× 548,151× 565,247× 609,631× 683,382× 598,684× 511,431× 440,928× 559,879× 566,424× 518,567× 454,183× 552,448× 515,778× 487,568× 491,816× 552,902× 481,598× 523,624× 412,532× 429,378× 295,116× 355,952× 442,731× 324,557× 374,982× 500,228× 417,380× 417,372× 412,416× 344,889× 303,190× 385,922× 413,435× 429,356× 288,454× 303,231× 329,741× 357,801× 420,917× 407,047× 371,763× 350,275× 313,690× 297,445× 283,816× 291,011× 352,246× 374,059× 352,040× 312,361× 228,024× 187,878× 188,950× 173,092× 188,476× 225,942× 262,793× 195,335× 226,714× 209,887× 206,873× 213,944× 162,735× 167,296× 119,085× 132,624× 116,095× 120,318× 161,313× 226,985× 245,537× 302,614× 205,673× 164,041× 190,367× 182,208× 200,760× 242,184× 195,765× 153,790× 118,896× 163,557× 197,833× 210,777× 217,797× 191,610× 176,094× 229,386× 244,878× 240,959× 226,228× 160,951× 184,428× 258,118× 252,268× 209,142× 203,302× 152,705× 126,581× 119,853× 127,383× 103,747× 113,923× 131,971× 126,523× 76,064× 36,294× 25,473× 26,012× 33,078× 44,762× 45,016× 23,555× 16,620× 12,676× 9,591× 10,445× 2,586× 3,284× 394× | 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× 14,675× 95,320× 412,088× 963,670× 2,785,816× 4,266,598× 4,999,442× 5,357,886× 5,289,816× 6,274,374× 10,057,570× 14,841,034× 17,937,410× 17,418,794× 15,584,216× 12,804,066× 7,471,408× 4,981,178× 3,504,832× 2,823,548× 2,266,618× 1,764,750× 1,340,368× 1,307,658× 2,258,458× 2,306,238× 3,093,286× 2,579,618× 1,861,014× 998,940× 753,472× 1,328,724× 1,102,288× 1,451,882× 608,766× 105,818× | 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: 150s: 151s: 152s: 153s: 154s: 155s: 156s: 157s: 158s: 159s: 160s: 161s: 162s: 163s: 164s: 165s: 166s: 167s: 168s: 169s: 170s: 171s: 172s: 173s: 174s: 175s: 176s: 177s: 178s: 179s: 180s: 181s: 182s: 183s: 184s: 185s: 186s: 187s: 188s: 189s: 190s: 191s: 192s: 193s: 194s: 195s: 196s: 197s: 0× 1× 1,239× 2,200× 15,592× 148,744× 275,450× 152,278× 259,245× 349,715× 688,701× 282,592× 159,748× 180,011× 1,044,543× 1,905,881× 2,312,042× 2,350,048× 2,794,007× 3,801,474× 3,379,301× 3,466,639× 2,916,003× 2,560,036× 3,040,325× 3,330,718× 3,497,772× 3,944,075× 3,983,734× 2,891,328× 2,843,534× 2,864,538× 2,254,758× 2,426,466× 2,144,830× 1,937,445× 2,047,684× 2,085,900× 1,753,936× 1,504,765× 1,544,695× 1,698,909× 1,792,436× 1,699,430× 1,558,778× 873,881× 475,593× 458,244× 608,677× 704,966× 519,940× 234,201× 147,888× 101,368× 67,358× 88,994× 235,300× 757,234× 993,676× 572,625× 178,062× 101,814× 25,283× 21,523× 37,998× 46,847× 20,192× 3,936× 3,900× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 311,824× 3,644,056× 6,948,078× 6,889,823× 10,013,915× 13,625,958× 14,044,631× 13,974,280× 12,039,418× 10,576,705× 10,885,946× 11,267,776× 12,100,147× 12,719,916× 12,356,335× 9,998,785× 10,524,628× 11,110,162× 10,321,888× 8,322,485× 8,621,687× 8,862,917× 7,964,756× 8,329,046× 8,292,755× 7,224,620× 5,925,420× 5,314,344× 4,800,159× 4,495,191× 4,403,559× 4,114,145× 3,626,235× 3,046,108× 2,238,104× 2,287,724× 2,230,318× 2,977,029× 4,569,847× 5,672,295× 5,309,776× 5,458,505× 5,573,815× 6,954,750× 6,014,856× 8,060,097× 7,721,811× 7,631,123× 8,296,874× 7,479,096× 6,914,475× 7,623,512× 9,904,074× 12,718,658× 10,724,087× 9,167,444× 6,792,758× 7,663,266× 8,283,824× 7,149,230× 5,791,236× 5,617,016× 5,804,165× 4,661,985× 4,403,198× 4,335,059× 4,915,248× 6,032,507× 4,912,091× 4,203,563× 3,077,103× 3,267,850× 3,292,281× 2,905,004× 2,619,445× 2,133,396× 1,742,900× 1,388,684× 1,200,706× 1,908,738× 1,755,936× 2,135,128× 1,528,334× 1,372,847× 1,032,755× 847,526× 495,328× 504,935× 598,302× 408,708× 188,393× 114,999× 134,969× 188,747× 188,290× 133,250× 139,229× 115,861× 92,627× 75,032× 66,997× 33,844× 45,260× 13,520× 2,680× 19,232× 14,400× | 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: 0× 1× 41,109× 424,332× 1,856,808× 4,618,384× 8,153,770× 10,779,312× 8,494,594× 4,310,174× 2,056,898× 1,685,648× 1,139,040× 299,264× 183,312× 45,036× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 847,190× 6,054,766× 18,031,040× 30,979,716× 44,557,644× 65,247,044× 82,749,222× 105,995,434× 106,607,116× 97,392,032× 89,675,466× 89,543,944× 73,302,766× 62,946,968× 50,591,290× 51,540,652× 53,436,238× 58,292,788× 73,423,998× 81,942,920× 82,359,028× 71,482,110× 61,267,700× 55,012,412× 45,572,142× 41,392,952× 42,684,948× 49,514,850× 56,736,818× 55,324,752× 48,415,654× 42,536,006× 45,452,468× 61,675,946× 48,848,912× 33,956,568× 28,753,262× 28,649,526× 29,096,606× 33,845,156× 23,752,550× 15,939,172× 11,173,496× 5,939,034× 3,627,754× 1,388,516× 143,266× 13,920× | 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: 150s: 151s: 152s: 153s: 154s: 155s: 156s: 157s: 158s: 159s: 160s: 161s: 162s: 163s: 164s: 165s: 166s: 167s: 168s: 169s: 170s: 171s: 172s: 173s: 174s: 175s: 176s: 177s: 178s: 179s: 180s: 181s: 182s: 183s: 184s: 185s: 186s: 187s: 188s: 189s: 190s: 191s: 192s: 193s: 194s: 195s: 196s: 0× 1× 269× 0× 0× 0× 0× 49,700× 638,356× 1,607,592× 1,201,638× 1,093,302× 1,342,634× 370,993× 355,165× 551,802× 394,198× 274,739× 179,755× 210,120× 161,750× 636,083× 7,173,714× 16,020,764× 16,787,836× 23,607,764× 32,251,521× 33,636,098× 38,536,388× 39,909,058× 43,995,022× 47,436,275× 40,018,881× 45,961,164× 44,236,712× 47,651,990× 46,337,034× 44,491,605× 40,455,090× 48,404,446× 46,826,243× 55,244,873× 49,338,030× 39,441,970× 37,021,102× 44,710,500× 46,951,748× 46,461,996× 51,186,688× 47,220,710× 50,977,235× 53,445,575× 54,632,833× 53,127,484× 53,877,480× 57,881,819× 51,035,133× 54,862,064× 45,937,610× 44,316,501× 36,291,614× 38,487,264× 33,215,663× 35,203,955× 35,504,531× 34,551,366× 27,691,846× 22,316,839× 22,724,031× 22,255,145× 22,286,006× 18,985,037× 29,338,020× 35,781,328× 39,140,750× 46,091,243× 55,566,922× 61,200,385× 58,984,775× 47,061,815× 47,223,038× 52,973,742× 56,065,165× 65,498,281× 60,512,717× 49,293,129× 45,140,385× 45,362,344× 45,993,134× 53,219,936× 54,093,228× 54,363,132× 51,409,501× 57,199,798× 64,467,698× 72,597,592× 97,600,956× 111,894,372× 104,213,235× 93,687,332× 86,969,815× 87,523,395× 85,807,232× 86,508,752× 76,160,645× 83,305,505× 96,393,853× 106,187,541× 91,541,850× 87,659,893× 85,336,581× 103,103,919× 104,876,359× 94,276,045× 83,009,493× 69,450,279× 64,421,141× 71,598,501× 74,837,512× 75,486,954× 77,410,437× 76,296,429× 71,676,268× 68,460,434× 75,942,315× 70,414,591× 68,965,176× 79,471,238× 89,324,754× 89,825,122× 94,373,050× 79,436,169× 74,328,404× 75,306,514× 79,914,554× 87,432,222× 96,991,689× 80,309,719× 72,049,747× 63,110,619× 53,310,486× 53,209,668× 54,433,122× 59,712,084× 57,602,638× 52,165,601× 46,952,539× 37,497,902× 47,342,701× 45,164,723× 36,781,221× 32,700,145× 31,905,888× 30,080,694× 30,749,572× 30,407,267× 25,042,656× 21,494,704× 22,599,890× 17,770,626× 15,582,904× 15,575,981× 14,201,224× 13,690,958× 15,736,103× 12,886,355× 7,793,895× 7,711,546× 9,754,333× 8,810,761× 7,176,019× 5,487,141× 5,053,025× 6,244,601× 7,469,317× 4,533,270× 2,032,686× 1,324,611× 1,622,150× 1,622,581× 1,270,806× 1,451,029× 651,118× 347,379× 168,524× 178,843× 81,540× 238,788× 441,744× 328,907× 154,880× 177,762× 94,362× 120,215× 211,470× 31,246× 13,700× |