| 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 |
| m | n | o | p | q | r | s | t | u | v | w | x | y | z | Α | Β |
| 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 | 8.53 step avg | 12.68 step avg | 9.22 step avg | 14.40 step avg | 57.79 step avg | 23.50 step avg | 93.61 step avg | 24.83 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 50× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 0× 1× 50× 25× 50× 0× 3× 159× 138× 300× 600× | 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: 0× 1× 50× 1,351× 672× 1,342× 1,332× 1,318× 1,300× 1,278× 1,252× 1,222× 1,188× 1,150× 1,108× 1,062× 1,012× 958× 900× 838× 772× 702× 628× 550× 468× 382× 292× 198× 100× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 0× 1× 50× 1,044× 2,904× 11,384× 29,734× 339× 0× 62,972× 188,662× 18,486× 675× | 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: 0× 1× 5,558× 8,759× 14,066× 31,226× 50,796× 89,520× 110,544× 169,212× 186,994× 278,003× 260,273× 311,405× 265,514× 283,344× 275,433× 259,997× 211,324× 199,280× 146,243× 122,269× 93,276× 61,170× 31,613× 10,918× 2,023× | 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: 0× 1× 50× 4,416× 10,215× 5,076× 21,915× 29,270× 68,193× 99,635× 34,263× 69,793× 33,535× 101,127× 83,707× 82,588× 86,417× 58,624× 75,224× 68,879× 60,050× 57,016× 120,596× 186,765× 288,663× 200,246× 222,731× 274,279× 338,482× 527,204× 1,018,757× 965,410× 1,142,088× 1,110,791× 937,905× 832,938× 692,143× 601,659× 690,834× 627,174× 802,416× 621,976× 489,937× 433,046× 333,417× 383,149× 408,326× 287,771× 235,776× 277,378× 394,156× 475,595× 337,992× 306,469× 324,886× 422,733× 368,761× 462,210× 393,536× 374,482× 341,800× 486,644× 571,677× 460,435× 600,943× 537,478× 443,395× 545,570× 594,219× 484,988× 318,066× 371,076× 311,835× 238,741× 165,816× 122,002× 115,032× 113,063× 40,535× 37,751× 53,324× 31,537× 15,677× 55,273× 60,742× 19,901× 13,473× 67,428× 80,551× 104,117× 96,673× 49,307× 26,047× 16,763× 21,437× 13,261× 10,286× 3,892× 8,510× 4,429× 2,471× 5,824× 30,760× 71,664× 81,272× 38,201× 30,285× 22,698× 18,515× 51,946× 126,821× 158,567× 130,282× 102,351× 87,505× 55,840× 159,373× 338,944× 313,410× 292,845× 246,895× 184,424× 178,208× 220,598× 107,162× 122,150× 171,490× 124,641× 135,144× 220,765× 280,582× 255,246× 138,918× 72,621× 83,122× 55,577× 77,735× 35,024× 9,627× 12,568× | 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× 50× 0× 0× 0× 0× 0× 0× 257,672× 666,896× 1,406,821× 2,195,517× 3,625,639× 4,865,118× 7,195,937× 9,941,056× 12,039,264× 14,260,176× 16,616,249× 19,572,381× 21,165,267× 21,788,569× 19,892,551× 19,219,522× 14,943,032× 11,722,668× 8,088,167× 6,272,085× 4,185,767× 3,246,459× 3,105,564× 3,105,472× 4,090,973× 4,284,183× 4,741,757× 4,728,338× 5,420,691× 4,302,534× 2,610,970× 1,850,038× 1,534,303× 824,058× 425,718× 191,047× 2,651× 675× | 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: 166s: 167s: 168s: 169s: 170s: 171s: 172s: 173s: 174s: 175s: 176s: 177s: 178s: 179s: 180s: 181s: 182s: 183s: 184s: 185s: 186s: 187s: 188s: 189s: 190s: 191s: 192s: 193s: 194s: 195s: 196s: 197s: 198s: 199s: 200s: 201s: 202s: 203s: 204s: 205s: 206s: 0× 1× 10,454× 35,706× 10,908× 7,416× 63,665× 245,840× 1,086,436× 1,667,449× 3,151,152× 3,882,362× 4,234,643× 5,502,560× 6,508,144× 5,581,172× 3,451,742× 3,850,294× 5,862,489× 5,704,323× 6,813,854× 7,491,779× 5,535,684× 5,912,643× 8,738,854× 7,328,314× 6,390,616× 7,256,032× 7,846,126× 8,617,562× 8,464,112× 6,694,480× 6,130,384× 8,000,452× 9,129,057× 8,420,870× 8,656,731× 9,717,963× 8,836,887× 9,172,245× 9,698,274× 13,027,850× 11,731,705× 10,264,803× 10,627,437× 10,990,924× 10,115,828× 7,819,547× 7,806,357× 6,968,421× 7,651,654× 7,901,013× 12,429,885× 15,262,262× 18,347,033× 15,319,048× 16,884,401× 13,340,018× 10,627,589× 13,971,569× 11,199,035× 13,574,042× 14,135,974× 18,063,848× 18,572,122× 19,783,994× 18,472,670× 18,388,593× 14,073,882× 11,380,729× 11,830,501× 14,039,220× 14,195,117× 12,937,917× 11,563,294× 15,204,844× 15,447,979× 16,594,701× 16,246,304× 14,267,884× 14,396,265× 13,292,713× 11,866,659× 11,581,777× 14,964,715× 16,515,701× 15,194,786× 17,617,505× 16,125,458× 16,030,775× 17,135,699× 15,006,069× 15,843,288× 12,897,328× 16,212,646× 18,307,818× 15,488,244× 13,836,901× 11,342,447× 12,357,219× 11,847,946× 13,232,814× 11,180,868× 13,516,891× 18,894,813× 17,811,336× 16,864,976× 20,219,394× 17,414,031× 19,853,331× 20,513,291× 20,924,947× 20,903,187× 22,861,373× 22,234,634× 19,300,847× 16,564,869× 14,614,780× 11,678,043× 13,403,127× 11,162,248× 11,807,359× 15,001,519× 13,304,165× 14,449,829× 14,130,901× 17,189,003× 18,605,554× 21,083,253× 23,002,688× 18,841,408× 17,258,974× 13,260,620× 10,635,681× 9,055,520× 9,075,109× 8,569,083× 7,150,813× 5,313,262× 5,029,397× 8,101,224× 8,674,670× 8,316,988× 8,585,078× 7,682,418× 7,263,214× 7,415,065× 7,425,262× 8,297,271× 8,997,341× 8,969,832× 10,611,591× 10,013,769× 11,360,302× 11,280,447× 12,304,655× 13,514,623× 8,475,540× 9,506,753× 6,635,299× 7,136,191× 6,676,068× 5,583,660× 5,081,264× 5,766,826× 5,170,525× 5,791,316× 5,594,029× 2,725,479× 1,740,067× 2,020,042× 1,771,976× 1,192,846× 930,084× 2,016,936× 2,756,601× 2,393,379× 1,513,151× 1,080,081× 1,347,175× 3,076,143× 3,567,018× 1,656,509× 673,050× 752,479× 1,442,889× 699,196× 624,783× 1,153,740× 1,175,525× 1,190,234× 407,914× 424,189× 671,142× 644,492× 871,037× 610,686× 339,655× 520,883× 722,720× 1,131,444× 1,234,541× 734,880× 90,319× 64,620× 50,892× 1,727× | 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: 0× 1× 303,770× 2,311,955× 7,449,761× 13,353,526× 28,115,851× 43,665,269× 71,168,924× 104,081,216× 140,579,835× 179,407,829× 196,452,978× 250,258,589× 267,101,602× 348,268,377× 385,622,127× 439,789,077× 484,714,004× 525,460,253× 503,424,017× 489,232,118× 452,387,218× 511,626,520× 581,443,661× 615,570,633× 626,518,991× 583,781,268× 576,717,045× 529,366,713× 418,271,313× 394,481,338× 341,842,969× 373,569,123× 346,629,347× 392,677,383× 370,607,410× 305,644,436× 228,396,595× 150,626,544× 98,237,183× 71,207,842× 47,900,068× 34,140,056× 16,194,971× 10,816,140× 4,804,916× 1,364,567× 85,932× |