| 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 |
| W | X | Y | Z | a | b | c | d | e | f | g | h | i | j | k | l |
| 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 |
|---|---|---|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.98 step avg | 12.53 step avg | 11.55 step avg | 12.57 step avg | 13.42 step avg | 65.86 step avg | 16.44 step avg | 69.85 step avg | 33.03 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 44× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 0× 1× 44× 22× 0× 0× 0× 0× 0× 0× 0× 6× 247× 231× 484× | 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: 0× 1× 44× 1,057× 525× 1,048× 1,038× 1,024× 1,006× 984× 958× 928× 894× 856× 814× 768× 718× 664× 606× 544× 478× 408× 334× 256× 174× 88× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 0× 1× 386× 1,461× 3,886× 6,870× 8,712× 2,674× 7,324× 305× 0× 0× 0× 36,900× 113,232× 12,301× 528× | 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: 0× 1× 3,884× 6,349× 10,010× 22,282× 36,060× 63,640× 85,505× 110,136× 124,021× 171,540× 155,772× 181,572× 175,246× 167,543× 143,135× 131,574× 94,458× 84,001× 65,524× 43,314× 22,306× 7,429× 1,582× | 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: 108s: 109s: 110s: 111s: 112s: 113s: 114s: 115s: 116s: 117s: 118s: 119s: 120s: 121s: 0× 1× 44× 4,848× 12,232× 26,370× 40,119× 21,625× 3,936× 0× 6,927× 25,084× 42,904× 42,726× 84,258× 119,018× 87,427× 33,810× 37,312× 54,751× 37,697× 27,918× 21,920× 16,721× 15,105× 25,621× 30,658× 47,588× 91,422× 39,406× 35,174× 24,916× 15,943× 26,174× 60,348× 126,884× 272,494× 207,974× 163,116× 219,778× 177,210× 179,960× 170,088× 190,016× 190,918× 241,064× 328,439× 392,036× 329,593× 342,461× 293,787× 267,951× 241,552× 198,267× 218,973× 191,336× 261,295× 262,733× 264,369× 295,928× 280,008× 294,214× 257,384× 192,889× 163,901× 132,925× 136,195× 131,722× 127,877× 141,630× 110,954× 129,897× 119,227× 159,574× 137,329× 169,465× 176,789× 186,027× 197,554× 168,121× 213,223× 169,726× 253,564× 234,760× 223,800× 235,270× 213,588× 244,758× 127,513× 109,263× 113,269× 167,177× 206,615× 209,634× 139,738× 124,637× 135,812× 122,185× 187,284× 153,534× 161,824× 122,704× 81,718× 85,516× 83,087× 141,905× 153,955× 157,089× 80,022× 75,305× 66,069× 78,136× 71,405× 68,088× 71,421× 67,759× 52,845× 16,374× 30,736× 28,294× 3,479× 5,712× | 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: 0× 1× 44× 80,960× 207,460× 560,864× 1,326,132× 2,409,438× 2,960,708× 4,273,191× 5,505,325× 6,635,412× 7,693,512× 8,836,718× 9,057,999× 9,300,551× 7,174,900× 6,438,661× 5,023,681× 4,236,487× 3,523,474× 4,180,742× 3,939,339× 4,488,762× 4,312,819× 4,157,596× 3,539,007× 2,237,857× 1,500,296× 926,260× 672,747× 295,314× 214,844× 49,497× 7,701× 6,801× | 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: 108s: 109s: 110s: 111s: 112s: 113s: 114s: 115s: 116s: 117s: 118s: 119s: 120s: 121s: 122s: 123s: 124s: 125s: 126s: 127s: 128s: 129s: 130s: 131s: 132s: 133s: 134s: 135s: 136s: 137s: 138s: 139s: 140s: 141s: 142s: 143s: 144s: 145s: 146s: 147s: 148s: 149s: 150s: 151s: 152s: 153s: 154s: 155s: 156s: 157s: 158s: 159s: 160s: 161s: 162s: 163s: 164s: 165s: 0× 1× 14,156× 32,952× 109,856× 172,695× 448,859× 465,936× 1,015,500× 1,123,561× 605,166× 520,045× 428,350× 242,796× 276,143× 779,076× 63,797× 53,994× 48,128× 1,440× 0× 108,480× 481,386× 1,672,695× 3,096,790× 4,127,266× 7,267,401× 8,152,731× 8,420,745× 8,696,635× 11,027,957× 11,823,145× 13,139,110× 13,142,380× 12,275,294× 11,578,893× 11,043,192× 9,480,575× 6,770,745× 6,927,182× 8,726,839× 8,428,037× 9,140,177× 8,222,187× 4,694,839× 4,528,816× 4,566,978× 5,313,515× 7,279,127× 10,904,216× 13,724,866× 12,913,292× 12,212,099× 12,403,548× 10,865,080× 11,590,823× 13,394,108× 12,940,974× 11,664,605× 10,722,637× 9,385,233× 10,619,842× 12,148,037× 9,635,252× 10,631,040× 10,827,122× 10,488,993× 11,028,058× 9,766,616× 11,094,575× 8,632,673× 8,020,451× 8,664,246× 5,058,496× 4,480,089× 6,142,325× 7,216,689× 6,703,127× 5,514,106× 4,825,957× 4,578,406× 6,371,498× 4,658,687× 3,716,502× 4,244,458× 4,399,857× 4,839,229× 3,652,054× 3,349,122× 2,634,872× 2,386,684× 3,113,082× 2,340,247× 2,658,858× 2,986,468× 4,402,996× 5,835,165× 4,238,822× 4,580,038× 4,978,959× 3,711,596× 3,264,913× 2,878,863× 2,961,877× 3,623,560× 2,098,972× 2,783,443× 2,165,998× 1,469,613× 1,731,772× 1,415,450× 1,061,333× 1,452,131× 2,346,008× 3,081,111× 2,685,566× 1,941,503× 2,248,534× 1,680,620× 2,181,503× 2,883,598× 5,305,403× 6,060,376× 6,346,210× 6,119,686× 5,766,049× 4,287,408× 3,600,839× 4,279,035× 3,794,892× 3,212,523× 2,106,928× 2,296,916× 2,055,652× 1,975,616× 2,751,685× 2,091,242× 2,577,328× 3,066,547× 3,449,988× 3,612,146× 2,214,098× 3,064,559× 3,101,516× 2,537,514× 2,340,309× 1,469,837× 1,667,762× 1,438,796× 892,939× 614,368× 1,356,071× 942,608× 774,521× 1,141,069× 1,124,974× 704,345× 751,521× 664,401× 226,588× 115,879× 154,344× 12,791× 22,384× 58,708× 1,068× | 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× 171,692× 1,097,272× 3,406,196× 5,676,686× 13,240,017× 20,008,186× 35,469,101× 52,288,665× 59,042,114× 69,886,482× 70,771,860× 75,950,338× 75,613,252× 109,804,881× 100,096,847× 106,462,222× 83,077,735× 54,752,647× 29,328,959× 9,696,128× 3,574,856× 9,270,582× 23,124,141× 45,177,215× 79,806,458× 107,714,157× 143,019,356× 143,728,286× 147,358,039× 143,234,916× 158,426,221× 164,222,527× 183,051,635× 170,400,706× 160,109,244× 143,112,783× 124,628,013× 125,604,696× 109,893,933× 110,182,952× 103,810,462× 103,607,749× 92,706,316× 95,065,473× 88,100,235× 69,949,782× 66,560,265× 63,593,568× 75,167,265× 69,318,918× 62,587,761× 58,864,258× 58,876,758× 41,841,906× 26,453,815× 21,734,231× 15,602,378× 11,709,162× 9,766,315× 7,339,248× 3,303,218× 1,995,517× 1,757,205× 3,610,543× 3,786,110× 1,673,275× 934,366× 340,354× 75,100× |