| 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 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.94 step avg | 1.39 step avg | 4.89 step avg | 3.72 step avg | 7.76 step avg | 10.65 step avg | 10.65 step avg | 10.77 step avg | 10.47 step avg | 33.78 step avg | 12.68 step avg | 14.90 step avg | 15.12 step avg | 19.76 step avg | 12.10 step avg | 18.99 step avg | 14.69 step avg | 18.16 step avg | 21.42 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 17× | 0s: 1s: 2s: 6× 93× 72× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 1× 107× 88× 174× 166× 154× 138× 118× 94× 66× 34× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 297× 588× 2,376× 1,067× 881× 441× 334× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 1× 561× 742× 1,218× 2,006× 2,486× 2,502× 2,366× 1,598× 2,708× 4,516× 3,660× 1,664× 306× | 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× 3,662× 5,862× 8,814× 7,248× 7,085× 8,055× 8,801× 6,030× 3,331× 3,549× 2,816× 1,614× 1,436× 1,670× 2,288× 2,182× 1,032× 2,361× 2,771× 2,997× 3,293× 3,115× 3,011× 2,538× 2,177× 1,210× 236× 828× 652× 282× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 1× 2,647× 4,752× 8,532× 10,978× 12,660× 8,040× 11,070× 16,670× 24,514× 38,200× 52,508× 54,156× 38,996× 22,490× 19,090× 13,008× 5,964× 1,794× 34× | 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× 15,945× 59,193× 63,203× 63,962× 73,097× 67,614× 69,030× 62,325× 56,840× 58,307× 68,960× 58,702× 53,592× 47,202× 39,623× 31,326× 28,070× 25,290× 26,419× 23,489× 18,395× 10,071× 10,259× 5,127× 2,302× 2,705× 3,892× 5,119× 2,946× 3,065× 3,824× 6,443× 1,798× 1,259× 3,058× 3,045× 2,459× 1,010× 786× 540× 250× 816× 216× | 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: 1× 35,289× 102,154× 173,212× 214,180× 257,680× 314,620× 268,930× 163,236× 158,616× 125,860× 131,602× 126,578× 155,132× 138,066× 81,916× 67,778× 87,850× 126,916× 107,394× 66,576× 23,568× 14,088× 10,520× 18,468× 20,450× 27,564× 53,442× 34,302× 11,566× 4,842× 2,016× 138× | 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: 1× 9,490× 62,522× 49,986× 73,807× 91,893× 121,453× 144,739× 176,213× 184,513× 189,234× 188,608× 179,664× 185,512× 214,101× 191,342× 117,045× 118,053× 168,854× 201,991× 238,311× 233,740× 204,858× 185,542× 168,443× 178,925× 181,690× 152,800× 89,265× 47,542× 52,360× 59,911× 61,320× 60,322× 45,199× 66,168× 56,385× 63,728× 66,129× 56,850× 50,220× 40,458× 53,318× 77,639× 146,427× 145,721× 159,198× 188,781× 181,492× 175,703× 163,084× 149,755× 199,985× 202,040× 193,885× 132,506× 69,027× 37,993× 32,395× 25,570× 38,150× 54,775× 53,030× 49,041× 77,581× 92,471× 83,786× 50,150× 66,377× 70,421× 88,597× 51,442× 32,727× 36,246× 32,159× 21,480× 22,702× 14,475× 14,709× 19,998× 30,494× 13,761× 10,011× 12,481× 14,276× 8,960× 4,738× 4,494× 2,732× 315× | 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: 1× 49,177× 304,822× 683,294× 816,804× 1,076,418× 1,247,214× 1,288,300× 1,276,238× 1,316,340× 1,411,740× 1,543,812× 1,471,176× 1,252,596× 986,960× 695,188× 743,786× 712,494× 856,680× 591,886× 300,524× 214,150× 180,248× 218,184× 264,866× 235,104× 272,114× 326,854× 294,480× 243,172× 154,594× 89,996× 110,282× 68,422× 56,422× 70,112× 35,034× 13,912× 784× | 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: 1× 66,074× 827,345× 1,116,797× 1,494,351× 1,798,770× 1,936,864× 2,133,089× 2,120,351× 2,122,000× 2,236,475× 2,363,909× 2,513,636× 2,852,352× 2,961,900× 2,517,026× 2,383,140× 2,144,826× 2,161,679× 2,077,732× 2,076,805× 1,996,120× 1,653,141× 1,462,010× 1,208,690× 1,035,410× 955,089× 911,153× 750,205× 579,090× 366,985× 279,485× 197,175× 185,501× 103,669× 100,116× 47,289× 75,524× 31,937× 17,280× 5,026× 7,835× 2,440× 3,944× 6,569× 8,838× 292× | 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× 31,289× 359,918× 1,022,458× 1,480,852× 3,208,762× 4,323,354× 6,101,552× 7,170,670× 6,697,278× 6,750,340× 5,732,450× 5,981,388× 5,687,008× 5,809,702× 6,244,960× 5,572,770× 5,729,076× 4,805,744× 4,456,746× 4,712,132× 4,709,936× 3,836,252× 3,277,230× 2,869,042× 2,550,220× 2,094,456× 1,965,296× 1,597,158× 1,675,306× 1,377,640× 942,850× 529,618× 285,764× 133,202× 36,634× 642× 154× | 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: 1× 119,788× 2,691,912× 3,509,165× 4,672,101× 5,729,248× 7,314,076× 8,831,131× 9,028,897× 9,310,041× 8,194,175× 7,030,848× 7,330,357× 9,293,925× 12,079,272× 13,975,391× 13,421,520× 13,249,788× 12,227,277× 10,316,787× 9,776,231× 9,986,695× 9,225,591× 7,767,198× 6,471,550× 5,329,977× 4,609,265× 3,261,810× 2,641,580× 2,628,502× 2,670,258× 2,200,019× 1,938,956× 1,779,978× 1,720,598× 1,307,733× 1,012,467× 1,099,515× 921,175× 1,231,297× 1,610,959× 2,088,523× 2,543,452× 2,362,360× 2,770,045× 2,649,060× 2,667,967× 2,891,317× 3,012,076× 1,956,207× 1,626,861× 820,046× 604,093× 507,120× 340,020× 225,839× 153,631× 112,633× 71,111× 104,482× 85,934× 43,869× 20,975× 5,386× 2,464× | 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: 1× 112,169× 2,212,850× 7,754,406× 14,751,470× 21,887,066× 37,918,532× 42,899,046× 50,283,358× 51,576,062× 54,340,930× 48,300,790× 40,613,714× 32,411,008× 23,813,362× 18,715,964× 13,758,746× 12,926,946× 9,662,678× 6,428,856× 6,728,306× 7,048,900× 5,953,704× 5,436,358× 7,483,586× 7,218,826× 6,561,380× 6,547,046× 4,667,876× 4,647,832× 4,253,056× 3,650,634× 2,313,052× 1,236,502× 780,692× 615,354× 186,134× 22,328× 3,200× | 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: 1× 347,900× 14,084,190× 20,852,221× 22,850,423× 24,197,884× 29,050,566× 37,066,407× 41,104,531× 47,508,481× 40,791,668× 31,455,795× 30,363,399× 37,601,021× 47,342,101× 57,074,470× 61,784,405× 63,816,496× 61,698,281× 54,250,539× 45,238,649× 45,463,833× 43,176,925× 35,473,315× 32,761,566× 28,731,799× 21,098,013× 14,290,865× 10,800,273× 8,738,613× 8,651,731× 7,560,226× 7,221,496× 7,274,075× 5,945,151× 4,570,920× 4,202,179× 4,281,414× 4,148,164× 3,735,737× 3,392,014× 4,609,266× 5,458,449× 5,756,851× 7,403,626× 8,414,681× 7,920,049× 8,571,334× 9,826,672× 7,585,621× 8,068,233× 5,619,104× 5,167,509× 4,331,521× 2,594,959× 2,077,512× 747,915× 277,386× 279,963× 272,539× 222,488× 301,724× 477,675× 548,624× 251,248× 15,309× 5,115× | 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× 142,763× 4,267,936× 18,015,588× 36,217,050× 55,264,896× 91,826,882× 110,739,052× 113,561,338× 122,893,204× 117,174,142× 105,223,586× 122,338,708× 137,255,298× 149,508,076× 154,838,848× 145,908,072× 140,592,246× 125,282,662× 101,903,398× 88,764,630× 67,368,544× 57,202,800× 48,140,374× 38,750,264× 28,020,632× 27,410,710× 32,138,716× 28,165,776× 24,057,602× 16,436,232× 9,668,178× 7,611,976× 2,498,020× 635,166× 534,810× 713,832× 1,411,904× 681,496× 401,828× 35,498× 3,486× | 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× 1,001,432× 68,196,742× 111,881,933× 97,980,945× 82,955,933× 101,971,273× 121,363,291× 158,387,863× 190,726,849× 193,474,610× 160,903,149× 137,929,675× 150,349,812× 160,269,775× 185,758,875× 219,230,167× 247,374,091× 256,538,750× 234,772,995× 196,733,616× 183,450,844× 157,486,131× 127,015,339× 126,809,427× 122,337,293× 87,774,103× 69,844,946× 58,672,029× 44,553,931× 33,773,075× 24,570,702× 24,661,875× 22,221,240× 20,580,063× 17,021,396× 13,677,561× 15,589,339× 13,911,639× 11,017,187× 8,563,671× 9,581,586× 13,011,298× 16,751,721× 17,551,578× 24,422,945× 24,210,265× 25,241,689× 26,780,742× 23,140,580× 27,652,204× 21,810,234× 14,940,428× 10,541,661× 9,804,466× 5,433,672× 1,805,497× 1,018,352× 590,774× 955,008× 792,972× 121,176× 21,399× 28,553× 25,242× 40× | 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: 1× 100,857× 5,064,000× 27,684,754× 58,148,424× 123,223,520× 185,124,366× 243,353,304× 280,541,580× 299,328,774× 292,125,448× 260,161,454× 230,623,596× 243,550,948× 232,181,430× 226,712,370× 248,607,366× 291,054,328× 308,978,566× 321,864,594× 279,059,296× 252,615,946× 218,154,044× 245,972,890× 263,848,706× 286,453,676× 268,438,478× 240,843,548× 227,448,740× 226,899,894× 292,139,592× 326,614,322× 302,315,676× 269,779,272× 204,578,024× 165,788,220× 147,511,024× 121,138,076× 116,148,698× 82,603,528× 49,339,260× 35,500,014× 35,112,136× 31,476,858× 19,719,390× 7,360,552× 2,038,178× 157,642× 11,154× 86× |