| 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 |
| W | X | Y | Z | a | b | c | d | e | f | g | h | i | j | k | l |
| 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 | 5.88 step avg | 9.27 step avg | 6.86 step avg | 11.48 step avg | 18.60 step avg | 14.60 step avg | 42.33 step avg | 20.77 step avg | 129.59 step avg | 55.36 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 32× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 0× 1× 32× 16× 4× 132× 120× 256× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 0× 1× 32× 577× 285× 568× 558× 544× 526× 504× 478× 448× 414× 376× 334× 288× 238× 184× 126× 64× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 32× 0× 0× 0× 13,600× 39,848× 5,136× 288× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 0× 1× 1,616× 2,897× 4,346× 9,674× 17,005× 23,339× 34,356× 42,431× 35,405× 40,772× 49,550× 42,482× 38,090× 34,302× 26,620× 18,077× 10,080× 3,928× 926× | 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: 0× 1× 32× 0× 0× 3,088× 12,586× 36,350× 23,130× 22,100× 41,505× 78,923× 115,119× 189,594× 119,140× 104,734× 199,039× 234,667× 299,489× 368,522× 128,661× 129,062× 83,933× 92,218× 74,182× 78,353× 56,155× 45,710× 42,465× 37,796× 25,562× 29,187× 24,240× 21,691× 16,723× 10,924× 3,934× 2,566× 4,056× 5,244× | 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: 0× 1× 32× 25,136× 55,612× 185,558× 370,208× 525,541× 682,456× 798,270× 1,060,494× 1,311,054× 1,348,806× 1,390,307× 1,118,258× 907,837× 593,737× 432,184× 391,126× 513,823× 554,402× 751,973× 828,112× 641,488× 378,721× 223,716× 77,921× 76,307× 50,944× 48,336× 27,740× 10,837× | 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: 0× 1× 2,936× 8,520× 0× 0× 0× 0× 0× 0× 17,485× 66,979× 198,149× 134,467× 70,974× 156,631× 485,880× 614,951× 777,816× 629,525× 645,903× 943,849× 1,026,510× 879,646× 1,051,409× 2,608,374× 5,255,675× 4,774,627× 2,217,046× 1,891,847× 1,805,498× 1,612,479× 1,696,823× 1,892,107× 1,853,260× 2,464,055× 1,227,214× 1,003,318× 780,587× 717,799× 905,971× 1,413,129× 1,195,198× 1,512,533× 1,541,059× 981,156× 1,126,064× 1,560,793× 845,263× 676,531× 1,635,237× 1,188,644× 1,489,585× 1,386,762× 786,096× 696,817× 1,238,447× 1,439,789× 1,852,094× 1,542,828× 735,426× 691,575× 499,763× 511,562× 619,739× 533,695× 340,116× 456,926× 312,393× 416,937× 259,916× 229,065× 211,789× 367,811× 899,552× 476,983× 398,690× 438,525× 272,060× 525,187× 192,187× 133,357× 252,388× 689,009× 842,431× 185,910× 199,109× 174,793× 254,974× 93,624× 37,850× 27,947× 32,342× 62,486× 2,232× | 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: 0× 1× 20,612× 135,492× 419,828× 848,619× 1,935,507× 3,176,984× 4,887,771× 5,952,594× 8,373,357× 8,968,159× 10,604,394× 13,923,613× 15,203,872× 20,241,377× 20,119,357× 21,113,408× 20,356,069× 22,371,435× 22,071,383× 19,778,672× 17,470,393× 11,454,538× 8,793,184× 7,658,366× 7,712,209× 8,540,271× 7,719,866× 8,961,743× 7,232,903× 6,698,917× 3,709,632× 2,746,044× 2,444,570× 3,156,131× 3,974,835× 3,855,810× 2,563,267× 2,078,106× 2,169,198× 1,501,822× 2,091,849× 3,055,350× 2,392,742× 1,110,915× 379,297× 246,462× 119,859× 2,782× | 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: 198s: 199s: 200s: 201s: 202s: 203s: 204s: 205s: 206s: 207s: 208s: 209s: 210s: 211s: 212s: 213s: 214s: 215s: 216s: 217s: 218s: 219s: 220s: 221s: 222s: 223s: 224s: 225s: 226s: 227s: 228s: 229s: 230s: 231s: 232s: 233s: 234s: 235s: 236s: 237s: 238s: 239s: 240s: 241s: 242s: 243s: 244s: 245s: 0× 1× 1,616× 2,904× 2,269× 0× 0× 0× 35,832× 151,397× 808,561× 958,241× 234,186× 213,442× 239,469× 990,746× 1,698,789× 413,366× 155,588× 35,795× 3,213× 7,587× 45,721× 122,984× 74,128× 320× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 620,911× 4,751,814× 17,662,285× 31,018,725× 33,375,448× 39,084,487× 43,405,457× 40,776,529× 36,078,966× 29,712,998× 29,877,848× 33,883,280× 52,203,744× 36,567,919× 32,151,249× 32,556,089× 22,197,639× 24,499,683× 27,529,165× 53,928,673× 50,454,247× 24,780,179× 22,731,064× 26,801,339× 25,921,178× 32,239,148× 27,103,223× 20,886,721× 24,200,915× 19,778,450× 19,100,102× 19,485,810× 24,510,305× 18,952,361× 17,186,158× 11,715,757× 13,247,319× 15,793,258× 17,186,356× 13,469,926× 10,183,198× 7,715,421× 6,820,347× 3,444,693× 3,557,220× 3,195,458× 1,872,047× 3,188,651× 2,317,525× 4,070,260× 2,140,580× 2,290,654× 3,778,613× 2,052,825× 1,433,828× 1,475,847× 2,011,989× 4,501,609× 16,751,679× 11,949,947× 6,818,341× 5,013,833× 7,085,823× 7,277,026× 12,755,508× 8,152,582× 5,020,834× 4,723,119× 8,003,698× 6,005,766× 2,813,920× 2,062,640× 3,657,945× 3,716,607× 1,400,584× 3,545,084× 4,888,455× 8,840,040× 4,456,109× 2,889,833× 4,510,525× 2,038,431× 1,422,006× 2,577,830× 3,519,218× 1,787,971× 1,377,570× 1,011,545× 2,093,998× 1,146,048× 1,610,171× 1,293,847× 4,448,824× 2,087,720× 2,142,978× 1,929,360× 3,323,923× 6,307,005× 3,529,617× 2,132,687× 994,992× 1,402,170× 3,788,719× 3,151,944× 3,379,766× 1,942,638× 1,635,570× 912,186× 906,466× 3,750,368× 14,959,354× 5,656,687× 3,915,869× 3,986,214× 3,442,190× 6,571,239× 4,825,451× 3,312,600× 6,961,925× 5,160,354× 2,191,618× 1,479,746× 1,308,885× 2,853,635× 7,088,329× 2,367,191× 2,108,239× 3,697,557× 5,671,333× 9,776,275× 3,592,227× 3,198,533× 1,939,954× 844,899× 1,731,361× 844,580× 1,181,062× 1,289,703× 944,778× 900,284× 825,032× 1,002,840× 1,652,229× 911,946× 507,903× 1,271,997× 621,647× 214,273× 190,159× 618,068× 144,900× 20,796× | 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: 0× 1× 2,936× 4,752× 0× 223,405× 1,244,792× 3,218,329× 5,728,352× 11,811,351× 22,449,693× 27,521,961× 43,116,612× 44,715,440× 43,167,081× 31,808,721× 29,935,389× 17,443,080× 14,152,987× 15,935,696× 18,604,941× 24,944,476× 25,958,013× 14,857,030× 5,936,874× 2,085,677× 484,078× 149,179× 0× 0× 0× 0× 0× 0× 0× 0× 1,953,641× 12,314,476× 36,000,132× 66,645,535× 111,645,926× 171,647,536× 213,363,184× 215,152,392× 176,722,422× 164,531,927× 154,860,440× 148,876,207× 130,768,799× 121,201,974× 105,752,820× 113,122,467× 116,524,823× 128,593,224× 148,768,147× 151,798,536× 160,640,218× 178,346,455× 185,794,906× 166,714,541× 144,982,860× 121,703,685× 112,970,571× 94,761,307× 101,075,350× 96,195,062× 90,987,260× 79,797,835× 73,773,741× 65,303,062× 72,870,664× 79,336,468× 85,464,269× 79,341,165× 74,841,939× 70,704,435× 55,469,182× 57,211,665× 55,879,878× 66,477,495× 65,002,223× 69,609,659× 57,191,620× 38,676,425× 24,848,279× 19,584,847× 19,141,323× 31,508,234× 27,769,616× 20,232,625× 11,188,517× 11,073,192× 8,899,698× 5,727,077× 3,831,185× 4,656,949× 3,730,652× 4,062,677× 5,732,910× 17,381,629× 17,653,202× 10,969,185× 4,300,804× 2,093,890× 478,582× 217,610× 52,272× |