| 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.96 step avg | 7.54 step avg | 7.73 step avg | 11.41 step avg | 9.67 step avg | 30.89 step avg | 13.44 step avg | 30.76 step avg | 20.61 step avg | 46.30 step avg | 27.42 step avg | 50.12 step avg | 63.86 step avg | 46.18 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 24× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 0× 1× 24× 12× 0× 0× 3× 75× 66× 144× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 0× 1× 24× 337× 165× 328× 318× 304× 286× 264× 238× 208× 174× 136× 94× 48× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 0× 1× 134× 175× 0× 0× 306× 1,085× 97× 0× 0× 4,160× 12,130× 2,219× 168× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 24× 0× 2,085× 6,198× 8,107× 11,822× 14,675× 11,242× 14,275× 17,742× 14,657× 9,565× 5,595× 2,265× 502× | 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: 0× 1× 344× 405× 0× 0× 996× 2,889× 4,060× 894× 2,038× 4,451× 9,787× 14,439× 18,822× 19,813× 19,076× 22,989× 14,173× 14,747× 19,324× 13,536× 17,924× 14,974× 16,926× 16,232× 14,301× 16,186× 14,119× 15,212× 14,671× 19,880× 21,233× 25,062× 8,463× 6,802× 8,663× 7,060× 4,650× 4,641× 4,447× 8,681× 11,460× 12,584× 8,767× 5,852× 9,680× 7,492× 9,357× 9,397× 5,746× 9,594× 7,660× 7,987× 5,613× 9,608× 4,473× 2,165× 668× 1,174× 590× 1,018× 2,327× 1,853× 3,576× 4,261× 4,766× 1,595× 561× 952× 88× | 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: 0× 1× 24× 8,940× 15,300× 47,575× 98,891× 138,652× 189,501× 234,554× 285,633× 293,181× 202,701× 94,978× 74,737× 70,611× 85,267× 69,759× 91,813× 108,829× 107,815× 93,991× 82,544× 84,413× 48,641× 47,055× 25,706× 13,801× 5,552× 9,110× | 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: 0× 1× 344× 405× 0× 0× 0× 8,408× 35,190× 109,167× 144,982× 129,453× 193,844× 357,411× 521,417× 622,279× 550,584× 594,983× 450,174× 369,870× 308,083× 258,893× 270,958× 221,622× 247,387× 223,412× 164,201× 217,260× 221,465× 217,406× 120,605× 99,562× 65,203× 65,202× 80,566× 44,269× 21,413× 11,992× 22,616× 46,588× 86,014× 103,068× 111,395× 55,733× 63,928× 113,658× 94,003× 34,651× 60,296× 122,813× 159,553× 253,701× 292,103× 379,136× 254,453× 151,520× 198,075× 138,674× 95,810× 96,150× 129,577× 129,669× 103,223× 95,129× 105,234× 46,466× 8,308× 3,350× 1,104× 3,509× 10,782× | 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: 0× 1× 6,504× 34,368× 117,072× 236,299× 443,707× 455,333× 505,173× 531,784× 768,637× 836,959× 1,066,136× 1,280,588× 1,741,853× 1,969,005× 2,272,808× 2,366,400× 2,427,839× 2,670,488× 2,529,288× 1,925,768× 1,133,416× 781,183× 858,587× 1,265,114× 1,307,994× 1,275,369× 990,002× 1,079,821× 1,087,897× 886,978× 630,903× 456,839× 424,927× 420,869× 365,866× 265,765× 204,384× 274,588× 293,795× 178,609× 100,743× 45,653× 39,430× 10,774× 1,584× | 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: 0× 1× 344× 405× 0× 0× 9,003× 73,472× 306,848× 545,536× 1,054,778× 621,078× 665,901× 546,580× 343,121× 381,637× 256,848× 140,814× 83,800× 25,177× 10,938× 7,774× 5,502× 52,162× 283,979× 1,377,129× 2,569,247× 4,497,146× 4,917,931× 3,008,877× 2,262,994× 1,817,231× 1,324,588× 998,879× 618,920× 639,515× 484,499× 437,803× 476,205× 1,788,435× 3,794,551× 4,049,735× 4,705,484× 5,090,108× 4,665,699× 3,321,592× 3,124,991× 2,879,970× 2,892,854× 4,664,053× 5,418,873× 4,922,590× 4,809,492× 3,954,329× 2,715,910× 3,593,079× 3,465,080× 2,947,260× 2,837,406× 3,458,445× 2,437,359× 1,606,669× 1,324,641× 1,464,759× 2,648,374× 1,884,336× 1,418,798× 1,198,187× 1,488,347× 1,055,704× 1,091,877× 522,774× 624,632× 712,155× 352,325× 306,064× 518,707× 140,464× 157,131× 67,165× 149,889× 9,942× 1,243× | 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: 0× 1× 24× 0× 0× 138,840× 756,972× 2,052,545× 3,346,217× 4,064,510× 6,668,542× 8,902,720× 10,460,335× 10,179,752× 10,610,186× 11,612,615× 14,202,378× 15,739,513× 16,288,115× 16,274,584× 17,880,073× 18,673,426× 13,192,535× 10,501,852× 10,300,022× 12,552,970× 10,425,434× 9,042,562× 8,706,202× 10,012,312× 11,625,830× 11,198,479× 10,924,226× 8,857,179× 8,402,985× 8,588,381× 9,800,760× 7,485,927× 5,339,433× 3,312,396× 3,017,159× 3,207,423× 3,989,270× 5,211,430× 7,136,721× 7,236,914× 6,702,379× 7,595,217× 5,787,127× 5,247,940× 4,899,277× 5,312,478× 4,365,592× 3,640,594× 2,372,765× 1,564,993× 1,013,997× 551,187× 178,124× 49,284× 22,316× 2,880× | 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: 0× 1× 344× 16,253× 157,342× 1,265,563× 3,757,242× 3,936,848× 5,109,460× 6,120,080× 9,860,917× 5,986,594× 7,122,257× 5,158,829× 12,620,054× 20,595,830× 14,446,538× 12,972,271× 12,539,199× 14,419,703× 11,383,734× 5,817,600× 2,669,298× 5,805,886× 9,399,600× 2,570,668× 3,759,376× 10,604,716× 8,037,555× 9,147,138× 9,138,157× 6,529,115× 4,996,756× 5,499,999× 3,324,267× 4,657,502× 3,609,837× 5,835,824× 8,455,968× 13,332,517× 15,476,391× 41,664,085× 30,509,795× 25,198,781× 28,746,644× 27,494,666× 43,328,574× 45,322,192× 49,177,752× 44,959,037× 38,424,635× 29,047,651× 36,582,761× 32,335,063× 26,521,895× 26,795,462× 29,940,626× 30,890,939× 20,881,303× 19,229,120× 19,799,884× 23,325,269× 13,629,430× 10,984,182× 13,957,893× 7,789,134× 7,299,023× 11,563,628× 15,327,662× 11,970,640× 8,162,576× 11,233,647× 13,066,446× 10,807,695× 11,373,147× 13,910,646× 11,160,884× 5,605,251× 5,029,134× 4,354,359× 4,278,026× 1,329,954× 1,368,121× 1,882,676× 1,883,409× 5,519,750× 17,240,530× 11,450,245× 10,227,124× 13,691,771× 9,809,932× 7,797,285× 5,281,835× 4,407,209× 5,313,809× 2,520,186× 1,951,582× 553,991× 247,827× 257,546× 762,310× 224,463× 36,085× 79,783× 22,631× 880× | 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: 0× 1× 24× 0× 0× 0× 0× 135,660× 1,019,033× 2,432,560× 3,208,743× 3,897,840× 4,293,070× 3,563,575× 2,362,984× 1,358,763× 1,804,249× 1,034,881× 449,648× 115,053× 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× 1,281,736× 12,073,173× 38,776,823× 64,527,378× 96,055,179× 137,521,803× 166,775,458× 181,554,174× 210,162,004× 203,905,302× 197,630,703× 188,363,909× 183,785,055× 175,406,060× 149,571,553× 128,458,414× 118,825,638× 109,046,991× 98,270,822× 89,179,050× 90,392,265× 85,136,907× 91,014,075× 84,209,262× 65,164,644× 59,812,309× 56,624,173× 54,923,155× 40,879,271× 34,292,011× 38,936,779× 43,500,136× 39,660,286× 40,034,018× 38,548,246× 27,729,028× 20,243,000× 13,961,387× 9,334,990× 5,329,938× 4,576,137× 5,514,766× 5,334,473× 4,168,172× 2,518,547× 2,241,127× 2,637,415× 3,143,877× 3,080,102× 2,582,696× 3,187,296× 2,815,466× 2,900,902× 705,972× 233,664× 130,723× 80,440× 19,776× 22,560× | 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: 0× 1× 15,464× 156,681× 212,092× 40,632× 381,387× 4,683,532× 22,457,566× 29,394,595× 60,317,199× 31,409,242× 37,972,843× 32,339,920× 66,450,005× 103,155,158× 124,759,269× 87,468,966× 66,537,032× 46,553,800× 79,462,893× 52,544,863× 33,213,598× 62,021,682× 45,735,095× 56,102,352× 73,214,740× 143,883,570× 143,179,700× 200,222,404× 129,349,719× 143,651,533× 123,652,709× 108,389,029× 157,812,684× 135,806,676× 137,278,036× 197,455,406× 177,227,082× 209,453,964× 182,576,595× 221,213,875× 273,771,497× 266,075,114× 205,776,123× 217,833,479× 177,946,876× 239,810,316× 338,843,365× 417,027,514× 294,430,524× 245,669,152× 251,108,696× 283,099,453× 274,707,071× 220,460,191× 252,646,425× 215,059,051× 174,907,826× 124,319,894× 121,258,176× 105,990,114× 62,306,234× 60,219,636× 48,602,023× 92,759,391× 63,542,116× 59,298,327× 40,129,946× 62,419,036× 107,736,129× 71,640,096× 38,667,650× 56,935,660× 99,176,896× 71,926,417× 53,577,079× 58,369,004× 64,646,432× 27,076,177× 14,591,737× 34,124,673× 24,867,551× 33,844,866× 33,862,948× 24,120,439× 20,044,167× 25,932,821× 13,830,265× 13,880,273× 29,338,459× 23,666,394× 5,848,664× 2,118,856× 1,144,377× 279,225× 334,466× 197,248× 3,976× |