| 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 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.95 step avg | 1.41 step avg | 5.67 step avg | 3.51 step avg | 5.79 step avg | 16.66 step avg | 10.79 step avg | 25.13 step avg | 11.61 step avg | 43.22 step avg | 12.94 step avg | 49.15 step avg | 19.45 step avg | 63.40 step avg | 18.62 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 21× | 0s: 1s: 2s: 7× 136× 110× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 1× 153× 130× 258× 250× 238× 222× 202× 178× 150× 118× 82× 42× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 661× 1,420× 5,720× 2,036× 1,751× 639× 422× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 1× 3,817× 4,872× 4,672× 8,774× 7,720× 7,292× 10,010× 7,706× 6,352× 3,478× 1,086× | 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: 1× 6,031× 12,551× 13,920× 7,956× 4,893× 3,942× 4,882× 4,814× 4,920× 9,081× 7,330× 4,874× 8,704× 10,716× 9,682× 11,795× 14,141× 18,626× 19,669× 16,942× 15,297× 11,537× 9,998× 11,226× 13,138× 9,039× 5,869× 5,534× 5,728× 2,631× 3,534× 1,005× 972× 2,350× 1,428× 1,254× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 1× 5,535× 10,868× 19,802× 20,104× 37,796× 55,928× 65,012× 81,260× 94,008× 111,090× 126,556× 150,136× 132,868× 126,364× 69,870× 39,820× 18,170× 17,708× 902× 242× | 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: 1× 37,071× 148,889× 162,132× 170,491× 126,515× 155,213× 148,103× 149,098× 125,674× 111,818× 77,795× 65,951× 73,819× 59,091× 68,029× 75,309× 66,596× 73,049× 70,001× 78,042× 70,530× 77,425× 70,004× 78,022× 74,659× 72,394× 74,869× 92,288× 85,006× 97,732× 89,756× 90,158× 74,161× 80,808× 82,182× 81,435× 61,505× 46,436× 37,878× 19,924× 24,559× 20,388× 17,525× 19,991× 10,338× 9,408× 14,849× 12,721× 8,823× 17,665× 15,931× 19,612× 29,286× 39,815× 49,205× 62,101× 46,089× 35,211× 23,940× 19,582× 26,298× 19,613× 25,775× 19,155× 22,008× 15,007× 10,632× 19,708× 23,932× 34,139× 24,694× 14,902× 14,694× 11,947× 4,649× 4,892× 2,012× 1,190× | 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: 1× 72,087× 250,286× 468,720× 648,410× 793,060× 771,058× 746,406× 757,076× 742,846× 788,798× 905,202× 1,122,402× 1,348,544× 1,265,822× 813,790× 400,884× 249,540× 215,118× 331,842× 436,854× 371,762× 307,182× 227,768× 126,398× 81,776× 29,386× 26,054× 5,636× 2,442× | 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× 39,045× 309,540× 454,072× 525,091× 483,173× 458,837× 418,118× 454,574× 394,420× 282,556× 298,885× 278,975× 229,920× 253,899× 209,653× 318,224× 449,308× 570,862× 424,197× 441,118× 367,709× 366,322× 596,501× 870,218× 838,968× 756,770× 613,653× 606,175× 517,468× 466,959× 615,481× 644,206× 589,098× 604,392× 665,496× 667,577× 712,446× 849,248× 724,369× 594,151× 538,492× 812,157× 776,636× 639,292× 591,536× 710,942× 843,229× 862,945× 1,033,625× 1,151,682× 945,563× 930,523× 648,730× 538,906× 560,081× 749,486× 747,694× 717,026× 596,859× 618,605× 548,851× 482,329× 458,413× 443,899× 390,032× 308,880× 240,530× 339,210× 430,156× 484,446× 508,270× 378,115× 324,546× 321,180× 298,213× 312,457× 350,992× 330,040× 251,538× 177,004× 154,468× 116,783× 121,679× 108,325× 175,144× 132,672× 109,775× 80,162× 78,582× 132,364× 124,844× 90,413× 52,091× 69,871× 81,414× 83,802× 26,874× 30,152× 38,274× 47,721× 45,515× 38,844× 12,458× 14,479× 16,698× 9,123× 3,641× 1,212× | 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× 131,057× 769,334× 1,969,544× 2,955,828× 4,754,010× 6,989,878× 8,775,610× 9,745,964× 8,967,130× 7,343,156× 8,121,802× 8,119,648× 7,163,642× 5,725,280× 5,556,898× 6,176,096× 6,498,544× 6,012,782× 5,155,382× 3,854,256× 2,286,962× 1,507,188× 1,336,092× 1,414,364× 1,502,624× 1,617,244× 1,411,512× 1,260,816× 1,102,676× 575,516× 200,872× 22,534× 238× | 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: 1× 131,488× 1,887,110× 2,940,390× 4,989,833× 6,125,212× 7,031,547× 9,021,217× 8,258,509× 6,367,473× 4,804,526× 3,938,261× 4,683,828× 4,865,465× 5,493,167× 5,493,882× 4,754,491× 4,977,059× 5,754,210× 5,636,641× 6,391,489× 7,041,117× 6,771,590× 6,210,950× 5,624,511× 5,374,748× 5,561,571× 4,325,325× 4,076,495× 3,812,371× 3,966,605× 4,954,076× 5,010,880× 4,435,993× 3,679,868× 3,143,907× 3,288,945× 3,516,907× 4,040,036× 3,558,762× 3,292,424× 2,931,754× 2,835,518× 2,623,973× 2,763,843× 2,826,115× 2,800,349× 2,556,021× 2,466,999× 3,069,789× 3,267,161× 2,868,467× 2,509,464× 1,833,328× 1,209,793× 1,101,109× 954,021× 638,061× 632,010× 827,014× 695,905× 641,958× 531,157× 507,578× 450,393× 665,755× 770,891× 1,055,544× 1,300,371× 1,348,642× 1,298,742× 1,810,471× 1,644,470× 2,208,034× 2,103,255× 2,137,612× 2,474,815× 1,939,599× 1,993,489× 3,134,228× 4,789,245× 4,701,382× 3,764,259× 2,685,696× 1,868,478× 2,322,879× 2,910,798× 2,195,872× 2,030,908× 1,293,311× 1,176,777× 1,180,593× 1,139,881× 1,434,097× 1,794,912× 1,531,263× 974,847× 653,261× 893,467× 916,927× 708,479× 528,838× 508,638× 469,529× 622,990× 667,622× 725,002× 795,754× 882,952× 936,609× 1,040,581× 967,342× 1,685,149× 2,301,954× 2,452,829× 2,139,050× 1,715,478× 1,650,779× 1,694,104× 1,640,491× 2,295,408× 2,310,278× 2,022,773× 1,294,846× 992,578× 1,106,900× 1,011,888× 888,132× 872,324× 577,686× 382,341× 456,630× 803,867× 755,725× 540,252× 837,611× 702,664× 544,450× 441,100× 709,533× 888,801× 1,491,294× 777,792× 736,388× 509,502× 216,025× 305,243× 289,164× 285,430× 159,141× 120,832× 91,080× 159,737× 71,688× 24,161× 18,814× 39,010× 17,792× 1,515× 3,901× 8,433× 990× | 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: 1× 588,317× 5,633,158× 13,551,432× 18,579,146× 23,978,402× 29,508,076× 32,619,996× 34,132,982× 39,035,102× 42,861,330× 39,008,802× 28,808,458× 30,527,740× 27,776,984× 21,318,576× 20,062,746× 19,608,366× 22,592,140× 25,552,442× 27,246,114× 28,226,548× 29,662,720× 32,482,378× 32,984,550× 30,306,728× 25,415,728× 25,938,534× 22,333,002× 18,588,182× 18,089,194× 17,872,236× 18,003,796× 17,557,196× 17,561,550× 18,982,188× 14,935,052× 12,609,398× 10,025,890× 5,634,018× 4,891,074× 3,918,758× 4,756,922× 4,965,774× 3,420,870× 3,127,396× 1,364,376× 818,942× 301,284× 145,588× 41,034× 32,544× | 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: 1× 290,198× 6,540,334× 10,379,700× 16,310,520× 21,197,686× 21,915,461× 23,421,581× 23,204,239× 24,248,551× 24,048,194× 22,376,208× 20,739,478× 19,140,608× 19,007,526× 24,834,596× 29,266,913× 28,579,896× 22,826,997× 20,730,503× 21,283,975× 20,994,599× 21,013,658× 21,738,376× 19,929,959× 21,302,822× 19,773,400× 20,822,633× 19,522,521× 19,244,541× 18,810,689× 20,105,131× 21,138,945× 21,695,164× 22,439,016× 20,590,599× 19,461,775× 18,819,738× 18,243,434× 17,914,886× 16,303,816× 13,932,661× 10,025,297× 9,300,985× 8,431,712× 10,222,909× 13,821,018× 14,693,157× 11,047,792× 9,998,714× 10,435,851× 14,285,012× 15,396,860× 14,046,038× 12,065,506× 13,049,458× 14,497,236× 15,651,044× 16,741,904× 14,050,948× 11,449,885× 11,635,869× 12,370,219× 16,923,020× 27,635,657× 32,049,892× 28,093,775× 21,513,450× 19,173,850× 22,461,384× 28,269,723× 32,614,067× 33,972,696× 25,709,094× 16,699,651× 15,793,912× 19,105,530× 25,647,619× 30,693,038× 28,081,677× 23,382,974× 21,531,117× 22,708,942× 29,829,908× 34,368,296× 33,961,490× 27,739,601× 25,237,043× 20,408,616× 21,425,370× 24,098,458× 23,800,787× 24,480,587× 22,233,812× 18,417,958× 16,166,890× 17,704,002× 16,873,385× 14,610,272× 15,048,725× 12,634,541× 12,247,991× 13,292,724× 8,782,801× 6,195,119× 4,626,258× 3,502,074× 3,964,906× 2,672,132× 2,114,421× 1,691,139× 1,376,028× 1,890,446× 3,035,127× 3,593,826× 2,783,155× 4,441,358× 4,636,045× 6,279,670× 7,175,106× 8,286,215× 8,760,587× 10,630,609× 10,039,466× 12,813,195× 16,649,822× 18,376,960× 16,097,616× 12,732,187× 10,529,938× 13,528,247× 14,121,299× 12,949,653× 13,748,073× 8,722,193× 5,588,468× 6,664,208× 6,234,736× 5,401,429× 4,050,944× 2,630,564× 1,845,080× 2,769,693× 2,523,272× 3,079,314× 3,403,374× 3,072,932× 1,607,457× 936,608× 562,803× 485,669× 354,207× 264,978× 302,189× 297,692× 634,180× 550,971× 242,686× 238,480× 513,688× 821,849× 1,270,072× 1,073,460× 1,529,898× 1,596,080× 1,784,815× 1,286,087× 900,505× 1,084,019× 1,576,832× 669,268× 597,234× 544,248× 210,996× 11,134× 1,144× | 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: 1× 1,347,913× 22,925,302× 71,691,700× 124,803,580× 169,503,354× 227,187,616× 264,315,898× 260,000,448× 262,746,934× 261,192,550× 221,665,624× 203,404,120× 220,693,784× 235,532,966× 246,253,488× 247,644,450× 237,486,228× 217,014,976× 191,116,274× 170,594,148× 139,851,556× 111,021,672× 79,846,026× 83,534,882× 78,262,888× 70,784,326× 63,397,918× 52,289,086× 65,534,972× 61,946,404× 63,039,654× 72,030,138× 80,104,410× 76,669,092× 64,094,590× 51,108,050× 41,743,966× 34,162,266× 20,733,484× 12,925,996× 11,266,542× 11,162,908× 10,326,184× 14,416,086× 14,070,596× 12,485,712× 13,288,402× 13,850,614× 19,229,938× 24,040,148× 22,703,688× 26,335,984× 26,491,814× 25,027,148× 31,290,422× 26,875,964× 18,091,472× 15,504,158× 10,645,314× 6,478,098× 4,132,072× 2,236,172× 2,089,360× 1,388,270× 908,568× 2,139,096× 6,826,174× 5,941,418× 4,766,758× 2,586,764× 933,024× 170,962× |