| 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 Cycle Start | 0.96 step avg | 2.11 step avg | 5.74 step avg | 1.90 step avg | 6.33 step avg | 19.27 step avg | 11.30 step avg | 22.26 step avg | 11.35 step avg | 14.25 step avg | 23.42 step avg | 39.53 step avg | 16.16 step avg | 27.43 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 24× | 0s: 1s: 2s: 3s: 4× 99× 78× 144× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 1× 361× 165× 328× 318× 304× 286× 264× 238× 208× 174× 136× 94× 48× | 0s: 1s: 2s: 3s: 4s: 1× 4,600× 13,390× 2,316× 168× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 1× 4,946× 7,665× 8,446× 16,126× 11,814× 11,759× 12,677× 14,414× 13,195× 9,398× 5,547× 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: 1× 10,424× 21,911× 27,730× 18,748× 25,833× 24,060× 17,858× 16,781× 14,913× 18,005× 15,581× 16,057× 20,853× 14,386× 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: 1× 17,844× 28,352× 57,172× 109,847× 149,498× 214,383× 236,050× 241,473× 263,716× 197,971× 93,624× 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: 1× 33,629× 128,379× 414,396× 472,862× 483,638× 483,355× 546,495× 486,093× 574,181× 400,052× 271,151× 308,257× 280,381× 284,652× 229,495× 203,129× 223,482× 138,480× 185,689× 216,712× 186,213× 103,211× 66,603× 56,804× 55,401× 58,488× 30,964× 18,971× 10,536× 20,227× 45,372× 85,930× 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: 1× 241,705× 878,780× 1,640,798× 2,366,137× 2,706,695× 2,463,662× 2,732,749× 2,398,600× 2,052,207× 1,800,209× 1,626,040× 1,777,649× 1,875,304× 2,023,865× 1,790,774× 1,577,550× 1,680,579× 1,785,348× 1,575,073× 1,245,208× 601,302× 295,169× 160,411× 167,653× 86,354× 90,143× 114,316× 101,946× 207,945× 236,649× 116,504× 105,872× 36,073× 7,830× | 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× 103,100× 720,703× 3,410,990× 6,709,242× 9,514,175× 10,226,195× 8,764,886× 7,475,273× 5,481,944× 4,831,216× 4,135,697× 3,652,588× 5,387,368× 5,928,549× 5,314,572× 4,922,368× 4,015,397× 2,931,170× 3,688,819× 3,489,234× 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: 1× 138,864× 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: 1× 112,017× 1,103,432× 6,501,224× 17,092,270× 26,142,347× 18,981,457× 20,434,732× 18,136,801× 17,991,534× 13,167,577× 7,001,141× 7,860,416× 10,636,235× 5,600,655× 5,833,777× 11,117,850× 8,148,033× 9,370,014× 9,163,017× 6,551,660× 4,998,734× 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: 1× 1,417,420× 13,092,206× 41,209,383× 67,736,121× 99,953,019× 141,814,873× 170,339,033× 183,917,158× 211,520,767× 205,709,551× 198,665,584× 188,813,557× 183,900,108× 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: 1× 173,834× 3,390,964× 27,927,678× 97,739,775× 197,299,810× 143,604,241× 118,580,564× 77,067,420× 111,940,278× 142,301,588× 188,932,468× 207,181,766× 162,723,934× 130,779,861× 247,673,095× 212,886,471× 207,959,466× 199,512,111× 240,208,263× 300,410,575× 292,481,485× 203,820,076× 235,734,421× 302,698,116× 324,035,053× 419,410,738× 471,274,949× 349,181,933× 283,358,464× 291,776,980× 335,068,857× 304,534,258× 245,506,254× 291,224,591× 244,362,417× 200,872,964× 139,322,479× 130,153,984× 116,839,961× 71,918,179× 65,059,328× 51,856,227× 96,326,822× 65,973,970× 60,935,839× 40,862,344× 62,609,454× 108,329,044× 73,221,604× 38,764,180× 56,941,556× 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× |