| Radix Character Encoding | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E |
| 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 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.93 step avg | 3.85 step avg | 3.79 step avg | 2.03 step avg | 7.20 step avg | 6.26 step avg | 6.11 step avg | 7.07 step avg | 20.32 step avg | 15.69 step avg | 12.89 step avg | 12.19 step avg | 35.10 step avg | 19.55 step avg | 12.99 step avg | 31.03 step avg | 18.43 step avg | 17.71 step avg | 12.49 step avg | 25.28 step avg | 14.13 step avg | 21.65 step avg | 12.36 step avg | 29.75 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 14× | 0s: 1s: 2s: 3s: 4s: 5s: 1× 14× 7× 14× 28× 56× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 1× 141× 60× 118× 108× 94× 76× 54× 28× | 0s: 1s: 2s: 3s: 4s: 1× 630× 1,757× 609× 63× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 1× 194× 419× 773× 1,482× 1,522× 964× 688× 622× 1,132× 1,942× 1,204× 498× 187× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 1× 991× 2,074× 3,528× 6,600× 6,284× 4,575× 2,259× 4,040× 1,264× 1,091× 2,200× 3,097× 687× 69× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 1× 5,693× 7,573× 11,146× 11,954× 14,028× 11,248× 13,969× 13,240× 13,389× 9,210× 3,257× 1,544× 28× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 1× 5,554× 18,291× 54,049× 40,442× 27,291× 24,656× 25,302× 24,639× 15,223× 13,690× 12,630× 12,139× 11,296× 8,563× 10,801× 11,112× 3,845× 246× | 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: 1× 8,850× 20,651× 36,393× 27,173× 18,348× 20,336× 15,046× 14,146× 16,107× 6,681× 8,783× 14,463× 23,025× 27,017× 25,837× 22,018× 22,977× 15,064× 21,423× 21,059× 29,674× 24,524× 19,286× 11,580× 12,347× 17,387× 37,077× 45,396× 42,462× 27,207× 27,141× 28,989× 36,312× 24,898× 16,484× 7,567× 9,228× 8,014× 4,915× 1,144× 160× | 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× 2,538× 16,133× 87,768× 79,803× 65,825× 49,863× 51,870× 63,844× 80,187× 75,014× 67,074× 56,843× 57,252× 87,402× 73,620× 99,815× 80,422× 77,684× 74,805× 77,108× 83,341× 108,829× 122,873× 87,772× 71,720× 56,613× 43,263× 22,356× 12,130× 6,857× 4,580× 3,145× 7,696× 2,189× 1,427× 1,594× | 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: 1× 20,881× 91,131× 190,083× 239,648× 278,249× 306,985× 316,290× 268,781× 228,867× 226,034× 212,599× 180,637× 114,569× 143,511× 135,697× 120,432× 95,070× 94,667× 115,148× 147,283× 153,222× 111,778× 106,497× 95,172× 114,355× 85,655× 67,877× 53,039× 24,259× 17,957× 21,312× 25,244× 22,689× 15,936× 8,553× 6,472× 820× | 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× 7,483× 79,477× 531,791× 598,152× 531,667× 482,187× 654,723× 699,361× 758,869× 635,620× 505,828× 355,173× 349,615× 335,660× 257,178× 192,647× 216,104× 216,072× 195,014× 360,441× 361,939× 361,478× 246,823× 197,938× 151,679× 98,693× 83,216× 71,913× 67,358× 31,167× 19,475× 2,622× 336× | 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: 1× 7,010× 50,436× 108,216× 148,804× 327,040× 322,037× 320,561× 290,306× 306,010× 402,779× 256,467× 210,420× 294,205× 380,830× 475,611× 392,834× 503,954× 574,005× 461,834× 356,423× 269,353× 381,814× 275,290× 143,730× 136,052× 192,979× 224,906× 227,925× 289,287× 212,347× 178,398× 152,345× 104,435× 156,898× 288,057× 272,832× 290,522× 310,489× 410,286× 400,604× 431,988× 454,873× 410,068× 445,142× 496,841× 445,401× 504,572× 494,607× 448,908× 361,111× 220,251× 181,523× 161,645× 176,134× 215,638× 205,592× 202,419× 219,153× 245,125× 246,306× 342,419× 365,450× 348,984× 383,350× 359,602× 304,413× 202,142× 52,342× 21,133× 2,836× | 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: 1× 6,567× 84,207× 999,570× 1,519,908× 1,550,081× 1,467,048× 1,720,883× 1,635,486× 1,214,495× 1,107,191× 964,586× 1,003,097× 866,482× 922,406× 915,289× 1,480,188× 1,573,649× 1,479,330× 1,019,882× 772,877× 708,789× 1,089,622× 1,251,474× 1,284,626× 704,408× 1,044,311× 1,051,556× 1,266,372× 1,468,584× 1,480,441× 813,884× 567,143× 403,379× 423,306× 456,619× 445,818× 397,297× 200,051× 293,915× 451,128× 578,820× 383,082× 176,409× 141,137× 159,798× 88,166× 43,664× 36,249× 32,110× 39,020× 72,128× 52,940× 60,415× 43,368× 40,044× 27,324× 18,209× 8,691× 3,566× 5,354× 160× | 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: 1× 84,182× 923,196× 2,511,861× 3,797,394× 4,082,493× 3,681,374× 4,879,510× 4,851,729× 4,518,097× 4,262,297× 4,330,395× 4,537,099× 3,951,110× 2,996,254× 2,397,311× 2,001,787× 2,093,420× 1,973,562× 2,386,859× 2,315,341× 2,820,952× 2,881,617× 2,272,168× 2,060,997× 1,410,256× 998,145× 857,951× 514,876× 445,832× 379,530× 191,543× 131,554× 17,923× 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: 1× 16,866× 271,282× 2,135,369× 3,468,770× 3,961,733× 2,186,689× 3,244,030× 3,385,101× 2,941,701× 2,520,801× 2,542,205× 1,915,348× 2,148,286× 2,101,353× 1,666,706× 1,412,503× 1,699,775× 1,569,031× 1,344,950× 1,417,064× 915,418× 443,251× 1,305,448× 1,207,863× 3,209,951× 3,975,706× 4,257,158× 2,731,084× 2,066,890× 2,408,562× 4,001,389× 3,467,612× 3,705,432× 3,125,153× 2,511,819× 1,925,736× 2,361,048× 3,396,452× 4,107,694× 4,159,661× 3,641,273× 4,022,435× 3,575,283× 3,223,349× 1,932,052× 1,898,851× 1,751,344× 2,983,170× 4,596,699× 5,256,921× 3,340,488× 2,416,253× 1,707,622× 1,353,178× 1,574,138× 1,615,624× 1,508,318× 697,063× 360,531× 354,536× 264,723× 98,555× 11,784× 5,458× 136× | 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: 1× 48,914× 926,992× 3,779,424× 7,754,654× 10,725,852× 12,115,614× 13,127,209× 12,152,640× 10,835,672× 9,380,332× 9,218,008× 8,393,314× 6,721,587× 4,874,255× 4,665,722× 3,908,686× 3,902,736× 4,292,935× 4,335,258× 7,159,787× 9,913,488× 11,975,608× 12,843,669× 12,914,923× 9,865,153× 8,409,783× 8,046,932× 6,995,292× 5,690,962× 5,263,111× 4,962,381× 5,738,712× 4,797,673× 4,329,972× 3,957,555× 3,636,343× 3,067,766× 1,871,564× 1,420,397× 789,453× 230,639× 72,603× 41,366× 27,588× | 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× 15,931× 356,504× 5,181,767× 10,078,090× 13,917,421× 15,784,992× 12,940,142× 11,412,151× 9,641,130× 16,461,560× 20,747,280× 29,454,735× 27,185,588× 29,739,525× 18,444,195× 16,188,068× 15,459,803× 18,865,068× 18,690,367× 20,367,023× 14,934,322× 8,908,022× 9,520,003× 8,210,298× 12,537,621× 15,652,867× 15,212,179× 11,682,197× 10,546,270× 9,049,202× 12,770,226× 8,244,546× 6,195,744× 4,120,728× 3,447,716× 2,688,982× 1,778,687× 1,781,207× 1,708,202× 834,520× 392,074× 128,654× 140,559× 19,013× 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: 1× 104,354× 2,948,668× 12,779,816× 27,944,075× 40,989,487× 45,565,810× 52,697,287× 46,700,712× 41,290,209× 42,393,545× 44,097,867× 47,716,223× 54,678,049× 49,220,772× 51,921,080× 48,303,587× 42,576,062× 41,128,470× 39,959,047× 33,812,992× 24,407,176× 15,050,792× 6,751,621× 3,243,246× 1,326,777× 738,233× 309,316× 89,170× 59,908× 4,848× | 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: 1× 56,847× 1,923,291× 26,497,477× 43,922,226× 54,814,396× 50,656,033× 33,098,243× 28,559,658× 20,866,869× 30,305,468× 30,534,123× 30,499,350× 32,384,581× 25,867,731× 17,142,845× 21,365,185× 28,717,692× 49,833,803× 45,283,028× 34,467,093× 24,741,190× 28,921,739× 24,790,557× 48,144,089× 56,730,553× 63,535,060× 34,313,164× 23,363,516× 15,926,869× 22,063,099× 25,421,358× 25,511,915× 15,420,894× 12,589,635× 8,892,823× 10,110,475× 10,419,535× 7,647,035× 6,110,088× 9,221,267× 14,109,469× 17,460,782× 14,414,846× 14,900,856× 16,600,033× 26,339,959× 28,137,481× 29,490,154× 28,082,724× 19,616,789× 14,718,855× 13,880,987× 16,144,467× 9,917,448× 9,732,038× 9,479,783× 9,459,197× 7,917,244× 5,607,929× 2,231,469× 1,237,219× 814,273× 430,688× 287,608× 191,851× 46,564× 19,328× 23,716× 11,082× | 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: 1× 69,882× 2,656,624× 17,914,628× 47,984,663× 69,013,491× 98,597,201× 127,725,130× 140,635,118× 153,673,240× 147,974,277× 133,281,410× 121,263,941× 115,218,444× 112,438,520× 116,087,855× 117,772,563× 102,352,377× 104,931,128× 97,339,968× 93,634,567× 83,871,894× 76,020,166× 59,322,990× 36,136,863× 26,446,568× 20,014,231× 16,733,273× 18,666,624× 16,679,631× 15,665,987× 11,796,385× 6,681,856× 5,882,604× 3,022,826× 1,415,641× 673,657× 328,312× 32,004× 2,860× | 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: 1× 56,301× 3,101,512× 52,284,891× 89,428,514× 106,014,343× 116,100,662× 87,986,353× 83,261,417× 86,726,305× 123,597,451× 145,103,808× 143,498,942× 129,024,060× 118,981,855× 98,389,566× 121,004,213× 153,761,709× 170,753,942× 118,226,421× 106,379,630× 88,231,700× 71,433,227× 68,247,059× 71,894,686× 52,611,891× 64,753,612× 54,992,939× 61,247,495× 59,361,535× 66,770,235× 66,818,950× 51,871,352× 58,400,880× 59,229,091× 106,213,726× 132,729,013× 160,404,723× 102,311,227× 76,805,611× 57,752,882× 75,225,120× 47,152,287× 26,730,049× 14,943,332× 11,438,603× 6,241,706× 4,837,732× 6,824,030× 8,689,659× 6,154,564× 1,906,364× 325,893× 62,447× 1,288× 396× | 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× 67,862× 3,667,432× 26,119,400× 114,570,412× 179,553,629× 258,500,796× 316,249,976× 406,851,282× 490,880,796× 529,099,832× 504,705,686× 430,538,889× 411,795,369× 393,371,864× 388,284,697× 401,783,201× 377,818,200× 298,478,395× 245,490,002× 150,055,896× 72,883,909× 41,746,210× 22,914,374× 16,934,777× 10,480,580× 5,229,493× 4,601,061× 2,592,835× 1,007,872× 457,591× 196,166× 130,548× 18,479× 2,580× 2,208× 4,500× | 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: 1× 98,778× 8,179,113× 140,933,700× 255,621,912× 279,359,606× 273,031,877× 200,398,467× 186,870,821× 210,152,830× 269,268,893× 311,491,607× 251,369,593× 199,238,846× 191,739,108× 191,395,410× 208,693,586× 165,440,249× 152,536,797× 120,990,685× 95,324,414× 124,349,201× 166,957,002× 170,424,694× 171,073,019× 184,992,497× 142,657,452× 134,645,297× 116,348,523× 137,848,923× 176,847,617× 237,073,247× 140,152,996× 92,367,584× 76,845,431× 100,335,188× 81,325,229× 78,029,920× 67,417,773× 87,192,522× 104,964,203× 181,112,032× 150,843,343× 147,497,270× 135,609,603× 131,638,132× 147,545,044× 172,749,019× 206,657,017× 204,895,139× 262,788,741× 195,243,993× 148,194,935× 143,471,044× 181,852,662× 179,065,395× 129,715,501× 129,534,331× 88,194,818× 51,366,780× 62,191,087× 44,170,393× 38,733,269× 33,871,261× 28,461,777× 20,219,826× 31,983,164× 28,108,421× 15,359,127× 14,238,613× 16,459,096× 15,266,843× 13,142,486× 5,985,492× 3,259,663× 681,598× 717,640× 2,115,050× 1,870,960× 500,269× 154,337× 70,829× 27,001× 5,768× 720× |