| 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 Cycle Start | 0.96 step avg | 1.42 step avg | 6.44 step avg | 3.38 step avg | 7.05 step avg | 33.14 step avg | 12.01 step avg | 28.80 step avg | 20.71 step avg | 35.91 step avg | 19.06 step avg | 72.55 step avg | 12.77 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 25× | 0s: 1s: 2s: 8× 187× 156× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 1× 207× 180× 358× 350× 338× 322× 302× 278× 250× 218× 182× 142× 98× 50× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 1,285× 2,910× 11,700× 3,445× 2,875× 873× 662× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 1× 3,747× 5,748× 6,584× 12,782× 17,154× 21,762× 17,894× 14,032× 11,572× 9,206× 7,778× 6,108× 4,582× 3,198× 358× | 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: 1× 4,380× 10,243× 8,694× 7,511× 13,823× 13,541× 12,135× 11,524× 16,481× 15,449× 14,458× 11,095× 6,388× 3,886× 4,998× 5,521× 4,683× 4,201× 4,782× 5,086× 11,175× 9,145× 8,730× 9,145× 10,386× 9,634× 9,148× 13,590× 12,364× 14,644× 21,336× 17,000× 16,968× 16,182× 18,085× 15,480× 16,225× 10,653× 15,703× 17,574× 25,209× 18,843× 16,584× 12,139× 12,854× 17,404× 18,926× 14,804× 15,888× 18,736× 15,002× 13,880× 11,747× 6,700× 10,922× 7,447× 6,365× 3,250× 5,422× 5,366× 4,311× 6,883× 6,604× 5,912× 3,036× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 1× 10,273× 23,812× 50,962× 62,042× 68,336× 81,376× 100,594× 149,528× 230,614× 254,772× 317,776× 318,604× 349,766× 432,244× 339,658× 325,806× 155,028× 60,964× 22,924× 6,186× 4,590× | 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: 1× 40,447× 173,177× 191,432× 244,318× 265,691× 217,702× 212,893× 235,985× 270,294× 274,166× 247,162× 236,831× 267,829× 323,623× 303,756× 284,997× 311,750× 335,686× 310,325× 257,427× 360,555× 421,701× 417,080× 348,623× 390,013× 377,518× 302,407× 269,468× 278,464× 292,029× 269,768× 256,771× 220,832× 226,547× 237,085× 237,246× 200,845× 188,696× 137,072× 131,835× 125,732× 138,961× 131,824× 109,903× 100,364× 118,620× 159,451× 115,850× 124,250× 137,811× 135,492× 115,906× 141,726× 200,437× 181,146× 138,088× 101,344× 83,818× 83,672× 83,933× 61,613× 73,128× 44,115× 47,331× 70,170× 68,342× 36,888× 47,803× 42,875× 28,411× 22,670× 24,092× 18,047× 25,763× 29,040× 48,304× 32,275× 6,974× 13,739× 7,630× 6,452× 9,967× 8,833× 4,653× 6,666× | 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× 21,687× 73,406× 154,188× 139,618× 329,790× 307,770× 428,626× 419,324× 796,018× 1,334,030× 2,327,052× 3,128,586× 3,642,000× 2,915,082× 1,746,096× 1,806,198× 2,146,254× 2,647,664× 2,362,178× 1,919,866× 1,623,596× 1,687,806× 1,678,552× 1,788,686× 2,246,868× 2,089,314× 1,540,348× 905,972× 985,050× 1,150,858× 1,135,258× 1,037,928× 776,058× 708,926× 501,202× 542,870× 711,852× 787,400× 868,098× 646,114× 253,892× 65,304× 43,556× 16,520× 13,794× | 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: 1× 290,046× 2,434,160× 3,322,072× 4,482,372× 4,916,207× 4,105,049× 3,580,498× 3,032,556× 3,170,500× 2,941,951× 3,301,513× 3,421,552× 3,625,978× 3,453,502× 2,866,614× 2,481,158× 2,286,051× 2,426,113× 2,475,000× 2,409,209× 2,262,052× 2,502,473× 2,952,763× 3,669,936× 4,416,383× 4,228,548× 4,465,702× 3,638,099× 3,122,980× 2,915,973× 2,995,544× 2,909,013× 2,925,233× 2,591,501× 2,817,091× 2,723,806× 2,892,990× 2,323,224× 2,269,650× 1,938,334× 1,818,351× 1,148,346× 1,184,872× 1,416,880× 1,344,246× 1,234,192× 936,889× 1,011,666× 1,347,494× 1,099,223× 1,188,625× 1,075,745× 1,045,179× 1,201,921× 1,526,839× 1,585,067× 1,263,024× 1,096,697× 1,058,442× 1,293,430× 1,095,132× 878,967× 713,969× 814,948× 878,706× 1,096,779× 1,409,450× 1,433,003× 1,533,015× 1,657,622× 1,643,170× 1,432,285× 1,423,564× 1,667,898× 1,758,116× 1,575,434× 1,353,330× 1,172,164× 1,183,357× 1,015,580× 549,292× 407,550× 317,409× 353,120× 520,797× 843,553× 1,093,151× 824,824× 514,269× 296,266× 282,541× 344,118× 404,767× 248,799× 180,829× 156,870× 159,409× 82,571× 179,841× 106,850× 290,539× 293,816× 152,714× 105,046× 135,782× 249,641× 329,481× 223,718× 134,572× 123,710× 113,898× 130,459× 177,685× 250,195× 122,516× 92,385× 93,982× 95,790× 72,076× 101,480× 60,321× 36,755× 66,808× 26,106× 25,882× 10,199× | 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× 390,565× 2,402,492× 6,109,302× 10,309,108× 17,039,680× 21,646,216× 22,304,622× 21,775,708× 18,529,510× 17,255,718× 16,535,892× 14,839,134× 16,242,484× 15,772,412× 18,236,730× 22,715,804× 23,682,656× 21,883,582× 21,909,828× 25,662,078× 27,011,240× 27,983,948× 29,933,046× 28,006,000× 22,712,416× 15,800,020× 11,911,378× 9,845,618× 7,832,150× 7,834,572× 8,620,732× 11,582,046× 11,126,464× 8,846,648× 6,273,252× 5,323,990× 2,850,840× 2,174,456× 1,966,192× 3,298,790× 2,773,038× 1,816,436× 1,600,210× 1,667,430× 1,420,860× 1,066,808× 1,595,814× 1,796,164× 670,588× 173,818× 46,810× | 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: 246s: 247s: 248s: 249s: 250s: 251s: 252s: 253s: 254s: 255s: 256s: 257s: 258s: 259s: 260s: 261s: 262s: 1× 967,091× 16,462,473× 31,408,799× 37,715,010× 34,486,899× 28,236,607× 26,255,675× 25,107,187× 21,916,356× 21,859,295× 17,423,715× 14,990,383× 15,053,725× 16,067,479× 15,741,741× 15,248,215× 14,921,697× 16,301,712× 16,515,913× 18,115,605× 19,417,937× 18,786,214× 19,329,186× 18,652,452× 19,121,067× 18,973,352× 19,811,091× 20,730,875× 20,122,243× 18,014,255× 15,486,391× 13,882,275× 13,013,476× 12,873,935× 12,069,819× 11,079,905× 9,496,421× 7,134,236× 7,455,040× 6,345,955× 5,121,783× 5,325,441× 4,234,500× 5,732,781× 6,728,014× 5,793,694× 5,784,857× 5,830,995× 6,660,967× 4,989,082× 4,989,731× 6,085,017× 6,768,936× 9,192,683× 11,602,209× 12,062,448× 14,458,355× 11,787,890× 12,392,154× 13,409,651× 15,890,738× 13,239,615× 10,442,116× 10,164,525× 9,172,367× 9,550,397× 12,185,720× 12,612,185× 13,419,337× 14,201,935× 17,040,974× 19,533,252× 16,867,961× 13,597,075× 13,692,546× 12,749,513× 11,889,258× 10,832,418× 11,726,328× 12,009,700× 13,598,261× 13,568,858× 15,098,801× 14,857,690× 14,503,297× 13,691,185× 13,322,046× 14,167,630× 14,661,843× 16,216,144× 15,813,649× 14,729,735× 13,077,407× 9,774,495× 10,180,677× 9,842,788× 8,727,848× 8,708,729× 7,299,731× 7,570,777× 7,755,379× 8,781,324× 9,166,313× 8,919,482× 7,447,807× 7,419,535× 7,412,940× 6,680,355× 5,308,419× 4,666,932× 4,286,494× 5,358,227× 6,153,992× 6,853,763× 8,954,097× 10,231,951× 10,185,352× 10,265,096× 7,266,715× 6,742,753× 5,478,198× 6,222,175× 6,756,352× 7,958,719× 9,970,205× 8,913,942× 6,954,531× 5,766,263× 5,725,221× 8,424,132× 7,463,724× 5,490,647× 4,735,736× 3,871,343× 3,094,894× 2,857,443× 2,567,131× 2,669,526× 2,270,061× 2,944,278× 2,345,737× 2,203,409× 2,176,362× 1,901,189× 1,677,791× 1,337,083× 2,343,549× 1,773,397× 1,843,400× 1,745,196× 2,704,032× 1,305,217× 1,466,494× 1,293,820× 1,733,648× 3,215,390× 1,948,740× 1,188,300× 1,055,463× 2,049,205× 3,148,617× 3,111,835× 2,970,280× 2,207,855× 2,620,324× 1,935,667× 1,884,080× 2,356,798× 1,995,898× 1,036,985× 1,333,213× 764,949× 1,326,583× 1,465,118× 2,285,683× 2,544,822× 1,778,277× 964,888× 1,026,975× 1,083,475× 818,805× 426,786× 320,131× 371,584× 446,293× 1,011,793× 1,829,526× 2,396,523× 2,421,870× 2,615,621× 2,132,447× 3,281,595× 3,705,111× 2,910,120× 3,387,765× 3,180,351× 4,263,429× 4,510,547× 4,690,704× 3,960,278× 3,824,453× 2,893,626× 3,173,020× 3,877,691× 3,079,329× 2,154,491× 2,060,434× 2,293,608× 2,014,375× 1,614,774× 1,671,426× 1,319,350× 1,407,498× 2,009,145× 2,253,124× 2,970,677× 3,152,084× 2,691,855× 2,392,541× 2,122,674× 1,835,435× 1,894,822× 2,117,251× 1,413,937× 1,619,117× 2,559,100× 4,259,957× 3,967,178× 3,341,990× 1,727,110× 913,792× 538,847× 444,015× 443,748× 933,773× 1,134,142× 798,442× 599,995× 620,408× 796,444× 676,327× 643,515× 508,128× 555,968× 569,273× 556,694× 639,749× 937,459× 2,145,055× 1,717,550× 1,377,891× 780,420× 249,026× 150,601× 133,977× 54,250× 111,872× 79,597× 45,722× 13,482× 4,426× 1,424× | 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: 1× 2,004,803× 22,453,452× 74,296,804× 140,981,240× 215,499,218× 333,913,966× 401,749,250× 428,348,858× 453,676,314× 452,232,148× 400,109,680× 364,656,238× 319,039,674× 255,880,086× 195,873,646× 164,156,374× 145,886,606× 128,991,940× 100,940,882× 85,158,706× 71,832,436× 63,343,198× 48,364,852× 51,277,204× 51,591,564× 56,346,280× 65,575,444× 63,299,432× 45,176,952× 42,895,812× 35,664,306× 29,835,054× 21,395,832× 16,295,432× 16,476,864× 18,232,518× 14,158,846× 10,425,014× 3,512,354× 1,926,526× 906,562× 554,008× 13,920× |