| 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 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.94 step avg | 2.05 step avg | 4.18 step avg | 1.98 step avg | 5.63 step avg | 15.49 step avg | 10.65 step avg | 12.46 step avg | 15.19 step avg | 17.88 step avg | 20.29 step avg | 14.47 step avg | 12.88 step avg | 15.28 step avg | 32.33 step avg | 20.31 step avg | 12.78 step avg | 18.76 step avg | 14.71 step avg | 28.36 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 16× | 0s: 1s: 2s: 3s: 3× 50× 36× 64× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 1× 177× 77× 152× 142× 128× 110× 88× 62× 32× | 0s: 1s: 2s: 3s: 4s: 1× 1,024× 2,964× 776× 80× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 1× 1,000× 1,550× 1,699× 3,487× 3,711× 2,148× 1,200× 1,281× 2,022× 1,634× 616× | 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: 1× 176× 769× 1,691× 1,329× 1,533× 3,740× 3,400× 5,283× 3,432× 3,622× 3,478× 1,951× 3,164× 3,569× 5,483× 3,331× 3,588× 3,250× 2,549× 2,155× 2,173× 2,491× 2,182× 749× 193× 416× 782× 1,153× 776× 349× 259× 351× 1,094× 659× 392× 505× 257× 414× 1,128× 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: 1× 4,328× 6,808× 8,664× 13,745× 17,654× 20,957× 26,773× 30,440× 18,603× 8,359× 5,821× 5,757× 10,067× 8,233× 6,881× 6,358× 5,232× 3,901× 3,064× 2,247× 2,212× 1,516× 3,599× 5,453× 8,125× 6,440× 3,425× 336× 158× | 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: 1× 3,506× 13,548× 34,993× 56,831× 50,067× 31,832× 36,264× 41,885× 23,777× 22,015× 25,524× 32,983× 34,804× 23,436× 32,398× 38,564× 43,542× 20,256× 25,548× 39,992× 33,031× 13,848× 22,839× 15,928× 5,294× 6,085× 3,226× 1,386× 808× 353× 228× 272× 193× 124× 90× | 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: 1× 14,984× 46,561× 62,522× 73,263× 92,402× 101,164× 93,275× 89,814× 91,134× 103,669× 145,030× 113,831× 97,895× 74,278× 48,417× 61,767× 37,532× 29,033× 24,327× 33,547× 31,248× 54,807× 55,294× 58,347× 56,538× 46,196× 37,180× 25,178× 18,690× 26,752× 46,142× 39,349× 29,150× 17,290× 15,667× 14,765× 22,266× 9,849× 3,197× 624× | 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: 1× 12,854× 67,188× 243,792× 284,250× 175,030× 144,834× 165,864× 110,929× 67,408× 88,554× 167,309× 143,763× 148,417× 167,904× 185,402× 296,572× 214,131× 340,547× 227,220× 203,492× 137,525× 145,424× 193,913× 192,759× 176,362× 130,171× 98,724× 69,523× 90,703× 67,386× 51,853× 43,595× 39,054× 31,259× 18,075× 23,321× 42,517× 26,977× 15,569× 5,486× 1,395× 6,607× 40,918× 40,568× 40,405× 43,503× 34,426× 22,164× 17,473× 6,160× 1,508× 631× 170× 150× | 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× 35,710× 132,638× 216,778× 234,966× 281,704× 252,305× 272,472× 376,241× 379,961× 317,994× 283,159× 359,268× 392,026× 427,878× 356,138× 420,075× 629,206× 523,281× 455,687× 409,348× 403,852× 389,368× 400,850× 438,495× 335,159× 352,208× 373,384× 396,950× 464,504× 547,754× 413,801× 295,435× 257,752× 253,396× 220,739× 201,579× 146,117× 92,768× 92,371× 120,836× 50,367× 25,498× 7,268× 608× | 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: 1× 22,891× 176,593× 786,516× 1,297,925× 1,642,251× 2,010,500× 1,903,135× 2,152,168× 1,681,831× 1,446,607× 1,021,342× 1,722,524× 1,830,555× 1,224,953× 946,412× 838,150× 700,829× 650,675× 682,869× 650,915× 586,014× 331,676× 535,606× 413,024× 360,150× 225,965× 411,090× 294,297× 328,449× 885,315× 624,337× 635,139× 384,960× 299,245× 143,202× 105,738× 56,006× 102,925× 103,209× 127,298× 48,070× 21,395× 7,296× 112× 1,444× 39× 46× 66× | 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× 37,168× 300,692× 954,158× 1,972,378× 2,635,850× 2,660,869× 3,726,554× 3,891,818× 4,501,441× 4,657,859× 5,088,673× 5,254,270× 4,593,744× 4,296,519× 3,239,280× 2,608,126× 3,040,141× 3,040,197× 2,598,659× 1,948,576× 1,606,760× 1,289,279× 901,567× 618,902× 436,214× 503,463× 419,555× 258,140× 155,913× 146,455× 132,030× 81,690× 68,488× 97,561× 82,305× 11,572× 6,544× 504× | 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× 38,211× 521,285× 3,173,915× 8,960,092× 8,621,080× 5,315,103× 7,262,554× 7,770,863× 7,575,919× 6,931,647× 6,059,704× 4,106,301× 4,435,238× 4,505,356× 5,166,202× 4,518,594× 5,200,500× 4,148,990× 4,723,864× 6,953,200× 3,956,666× 4,115,724× 4,029,033× 3,386,195× 3,817,928× 2,541,182× 1,873,545× 2,676,350× 2,973,608× 1,837,589× 1,446,668× 1,029,318× 577,514× 992,864× 774,826× 494,977× 255,244× 238,056× 242,016× 602,425× 397,031× 211,848× 270,479× 428,206× 154,588× 60,361× 45,025× 3,914× 876× | 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: 1× 22,696× 291,180× 773,537× 1,063,801× 763,090× 1,916,383× 1,592,837× 1,175,668× 1,430,200× 2,158,822× 2,386,898× 3,159,033× 3,905,646× 3,794,334× 3,390,028× 3,598,769× 4,063,847× 3,837,820× 4,150,023× 5,042,918× 4,289,442× 4,514,087× 5,717,530× 5,960,163× 7,037,883× 8,468,693× 8,993,743× 9,395,628× 9,570,167× 10,855,450× 9,896,418× 9,742,396× 10,461,330× 10,973,003× 11,890,307× 12,327,566× 13,265,369× 12,036,894× 10,827,959× 9,302,051× 7,530,328× 6,994,156× 6,458,953× 4,708,957× 4,617,967× 4,635,995× 3,886,112× 3,144,505× 3,069,121× 3,581,744× 3,301,181× 2,726,484× 2,490,537× 2,348,185× 2,620,499× 1,587,606× 967,664× 769,785× 660,605× 264,853× 93,446× 33,350× 4,552× | 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: 1× 51,511× 808,082× 6,260,295× 21,664,287× 19,442,016× 15,894,749× 14,851,001× 14,369,566× 15,815,532× 14,099,167× 14,208,047× 13,434,284× 20,512,956× 22,103,945× 20,666,240× 25,060,217× 22,924,549× 21,931,863× 23,415,521× 15,712,631× 15,216,541× 17,503,664× 16,475,268× 18,029,530× 13,851,570× 14,660,866× 23,858,718× 20,561,776× 12,038,934× 12,096,330× 13,323,887× 15,404,712× 14,650,066× 8,368,089× 6,444,850× 5,788,583× 8,489,161× 12,593,430× 8,713,745× 4,967,936× 3,094,860× 3,156,861× 2,571,774× 2,282,951× 607,842× 828,730× 591,719× 1,453,591× 214,720× 13,226× | 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× 225,304× 4,501,840× 15,125,235× 29,927,279× 46,409,709× 74,743,599× 73,621,883× 77,742,725× 88,081,470× 91,589,621× 76,563,682× 78,396,459× 78,850,986× 75,516,095× 58,799,297× 45,777,630× 34,396,723× 29,925,288× 25,097,667× 22,156,123× 17,542,356× 16,043,219× 18,096,075× 15,501,760× 11,835,072× 10,118,959× 6,999,288× 6,638,429× 4,463,636× 4,123,718× 4,612,028× 4,730,261× 4,556,687× 1,762,727× 1,400,686× 1,990,760× 1,718,968× 1,160,484× 1,461,446× 969,085× 891,248× 560,784× 650,516× 383,764× 178,164× 193,220× 413,588× 239,788× 89,400× 27,808× 570× | 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× 166,260× 4,375,378× 34,521,848× 113,237,339× 133,340,669× 99,041,386× 82,858,611× 77,876,021× 66,106,338× 81,661,760× 83,916,692× 95,175,251× 80,581,699× 48,497,511× 46,825,452× 46,499,058× 55,261,046× 56,984,783× 65,724,708× 56,673,557× 54,984,611× 69,545,050× 63,545,635× 59,309,787× 50,296,208× 58,869,679× 58,862,595× 44,878,095× 35,841,746× 38,537,177× 22,509,991× 20,505,139× 24,036,209× 22,078,432× 12,465,672× 14,395,929× 8,284,071× 16,715,201× 20,186,446× 20,640,478× 13,504,781× 10,867,899× 5,091,206× 7,239,055× 8,642,199× 17,568,312× 19,789,438× 8,928,281× 15,381,866× 15,175,982× 10,412,082× 6,743,266× 8,595,511× 3,919,304× 1,780,068× 1,163,846× 2,154,750× 1,002,366× 80,947× 37,043× 69,293× 208× 150× 58× | 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× 237,336× 6,071,796× 26,142,980× 62,177,085× 88,188,662× 164,531,629× 206,248,637× 210,552,257× 235,011,165× 286,598,910× 246,612,437× 223,304,351× 213,539,700× 209,409,905× 226,143,134× 197,205,782× 205,238,329× 166,713,368× 143,167,572× 118,006,826× 111,844,719× 94,752,020× 96,671,661× 93,111,961× 96,848,285× 90,642,988× 75,630,137× 54,372,964× 37,918,357× 27,770,686× 19,173,767× 10,317,955× 6,314,624× 4,315,692× 2,963,945× 1,424,944× 613,349× 131,969× 7,065× | 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: 1× 232,915× 10,169,410× 95,243,956× 429,503,701× 408,220,164× 347,836,929× 185,814,244× 150,118,896× 149,404,165× 208,071,943× 183,546,462× 234,790,024× 158,699,163× 181,363,387× 131,807,889× 130,358,357× 117,280,080× 131,635,909× 133,879,088× 117,922,390× 104,979,113× 141,924,698× 142,844,489× 112,537,050× 139,703,865× 67,284,391× 109,558,299× 64,967,921× 91,198,946× 129,313,708× 143,257,709× 109,672,998× 75,851,093× 74,467,199× 73,635,488× 58,602,740× 58,939,449× 60,743,369× 52,910,153× 63,475,764× 63,160,242× 32,675,858× 23,905,311× 20,706,792× 29,457,203× 61,821,679× 72,412,956× 72,466,275× 101,254,673× 120,575,407× 80,204,091× 75,875,755× 51,469,251× 42,330,162× 55,922,914× 44,360,211× 31,543,601× 45,041,291× 56,962,164× 28,181,560× 20,429,685× 29,633,933× 52,979,423× 51,571,488× 45,557,148× 56,879,161× 40,516,987× 31,570,542× 28,608,483× 20,579,131× 19,047,476× 14,098,990× 11,654,414× 9,891,174× 9,258,939× 6,288,731× 3,436,915× 8,000,773× 5,870,513× 4,474,552× 20,581,603× 5,580,013× 4,295,738× 20,730,143× 101,667,641× 29,390,491× 10,908,725× 6,754,722× 28,613,569× 31,773,837× 40,765,711× 9,590,046× 7,831,363× 9,289,767× 6,077,716× 5,210,427× 1,721,337× 2,113,031× 2,248,891× 177,604× 102,286× 2,376× 1,704× |