| 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 | 19.48 step avg | 11.62 step avg | 14.07 step avg | 13.89 step avg | 63.44 step avg | 26.82 step avg | 207.79 step avg | 22.42 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 47× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 22s: 23s: 0× 1× 47× 2× 79× 60× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 10× 485× 492× | 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× 647× 598× 1,194× 1,186× 1,174× 1,158× 1,138× 1,114× 1,086× 1,054× 1,018× 978× 934× 886× 834× 778× 718× 654× 586× 514× 438× 358× 274× 186× 94× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 0× 1× 47× 0× 0× 0× 1,298× 2,224× 5,948× 14,158× 15,400× 8,239× 16,611× 16,060× 36,830× 65,376× 32,364× 13,514× 7,682× 5,724× 1,716× 6,708× | 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× 4,671× 9,242× 12,526× 26,514× 43,024× 75,890× 97,528× 135,482× 153,346× 230,336× 203,470× 235,540× 218,430× 218,086× 205,848× 188,550× 146,668× 129,364× 99,052× 77,444× 55,120× 25,918× 6,910× | 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: 0× 1× 3,587× 4,900× 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× 43,972× 109,656× 101,372× 88,736× 82,902× 123,268× 183,208× 220,497× 272,676× 372,021× 253,737× 240,130× 227,468× 206,388× 289,574× 293,815× 351,457× 419,440× 440,424× 481,189× 455,991× 410,676× 482,328× 455,573× 346,124× 429,675× 375,233× 455,001× 481,426× 458,719× 464,762× 434,530× 449,368× 343,293× 360,550× 399,313× 509,699× 446,586× 499,309× 513,409× 547,770× 529,036× 505,262× 581,867× 531,586× 475,912× 407,348× 393,208× 431,861× 432,514× 472,489× 523,843× 448,536× 359,662× 303,301× 241,105× 185,813× 186,680× 158,594× 194,754× 186,388× 144,666× 190,615× 109,944× 140,238× 148,235× 122,521× 104,292× 124,401× 71,894× 37,362× 18,456× 33,550× 15,236× 16,558× | 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: 0× 1× 26,411× 98,500× 272,636× 474,690× 740,562× 877,906× 1,440,714× 1,834,574× 2,427,108× 3,155,772× 3,705,234× 4,132,300× 2,311,150× 1,080,796× 529,588× 236,232× 99,858× 18,234× 505,712× 1,277,750× 2,548,678× 3,843,154× 5,877,088× 7,890,978× 11,591,838× 15,204,788× 16,198,748× 15,338,914× 15,745,332× 16,776,678× 14,714,714× 11,490,308× 6,083,912× 3,806,282× 2,310,850× 1,429,870× 623,100× 379,600× | 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: 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: 207s: 208s: 209s: 210s: 211s: 212s: 213s: 214s: 215s: 216s: 217s: 218s: 219s: 220s: 221s: 222s: 223s: 224s: 225s: 226s: 227s: 228s: 229s: 230s: 231s: 232s: 233s: 234s: 235s: 236s: 237s: 238s: 239s: 240s: 241s: 242s: 243s: 244s: 245s: 246s: 247s: 248s: 249s: 250s: 251s: 252s: 253s: 254s: 255s: 256s: 257s: 258s: 259s: 260s: 261s: 262s: 263s: 264s: 265s: 266s: 267s: 268s: 269s: 270s: 271s: 272s: 273s: 274s: 275s: 276s: 277s: 278s: 279s: 280s: 281s: 282s: 283s: 284s: 285s: 286s: 287s: 288s: 289s: 290s: 291s: 292s: 293s: 294s: 295s: 296s: 297s: 298s: 299s: 300s: 301s: 302s: 303s: 304s: 305s: 306s: 307s: 308s: 309s: 310s: 311s: 312s: 313s: 314s: 315s: 316s: 317s: 318s: 319s: 320s: 321s: 322s: 323s: 324s: 325s: 326s: 327s: 328s: 329s: 330s: 331s: 332s: 333s: 334s: 335s: 336s: 337s: 338s: 339s: 340s: 341s: 342s: 343s: 344s: 345s: 346s: 347s: 348s: 349s: 350s: 351s: 352s: 353s: 354s: 355s: 356s: 357s: 358s: 359s: 360s: 361s: 0× 1× 20,343× 91,370× 70,468× 27,216× 81,140× 84,330× 221,340× 213,791× 257,942× 137,453× 256,040× 449,168× 865,448× 978,522× 683,723× 1,085,255× 1,131,174× 1,026,998× 820,411× 751,668× 715,327× 563,705× 114,046× 189,546× 318,488× 170,438× 218,574× 149,597× 10,060× 9,880× 28,340× 32,207× 41,370× 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× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 0× 441,068× 2,088,342× 2,038,528× 3,095,953× 3,314,678× 4,394,649× 4,122,578× 3,598,698× 3,390,647× 3,302,504× 3,396,159× 3,413,655× 3,667,737× 3,311,416× 3,141,389× 3,065,350× 4,230,222× 4,491,630× 4,195,486× 3,469,482× 3,148,028× 3,357,143× 3,329,518× 3,070,413× 2,606,720× 2,667,657× 2,380,149× 2,728,796× 2,868,520× 2,398,769× 2,013,353× 1,852,922× 1,747,576× 1,835,166× 1,314,815× 1,545,251× 3,496,203× 4,021,131× 4,348,886× 5,007,001× 7,159,591× 7,668,586× 8,034,898× 6,120,532× 4,946,813× 4,904,393× 5,647,436× 7,268,534× 7,424,163× 6,552,652× 6,484,109× 6,025,386× 5,166,805× 4,333,891× 4,544,277× 4,729,070× 5,331,264× 5,474,345× 5,442,485× 5,367,357× 5,260,412× 4,949,174× 5,488,096× 5,071,886× 5,329,270× 4,998,528× 5,225,584× 4,753,106× 5,040,656× 5,680,673× 6,324,220× 7,493,490× 6,496,281× 6,005,678× 5,585,084× 6,105,584× 4,724,893× 4,517,041× 4,795,358× 4,586,056× 3,934,432× 4,876,392× 4,710,870× 4,921,543× 5,217,264× 5,216,521× 4,531,821× 5,212,479× 6,257,664× 5,914,303× 5,175,247× 4,957,392× 5,908,480× 6,239,968× 7,661,260× 7,170,761× 6,619,064× 6,200,732× 6,241,490× 6,173,017× 6,620,234× 6,514,484× 6,513,201× 6,345,660× 6,812,140× 6,651,693× 6,248,278× 5,556,254× 6,149,574× 7,460,371× 7,701,700× 7,238,205× 7,006,946× 6,891,759× 7,129,734× 6,004,984× 6,096,441× 5,639,237× 5,969,760× 4,519,313× 4,445,112× 4,845,980× 4,564,971× 4,701,868× 4,951,049× 5,411,536× 4,861,188× 4,250,801× 5,334,874× 5,161,893× 4,195,654× 3,250,977× 3,767,077× 4,566,449× 4,184,609× 3,310,374× 3,188,926× 3,330,401× 3,070,805× 2,402,258× 2,538,556× 2,658,275× 3,696,583× 3,046,940× 2,662,899× 3,235,343× 4,038,156× 3,555,592× 3,466,491× 3,436,579× 3,615,459× 3,867,602× 3,880,145× 3,157,756× 2,983,318× 3,888,519× 3,864,002× 3,905,730× 3,991,220× 3,619,690× 4,363,051× 4,685,615× 3,965,766× 3,622,593× 4,055,559× 4,449,732× 4,885,849× 4,921,208× 4,340,940× 4,031,675× 4,199,744× 4,643,966× 5,240,429× 5,599,955× 5,095,898× 5,056,668× 4,526,290× 4,972,217× 5,697,382× 6,462,404× 5,304,547× 4,578,130× 4,293,433× 4,940,637× 4,915,533× 4,920,611× 5,044,893× 4,526,100× 4,998,840× 4,118,260× 4,427,002× 4,743,989× 4,259,843× 3,639,142× 3,962,576× 4,814,229× 5,185,719× 5,502,964× 6,123,728× 6,458,099× 5,907,644× 6,319,600× 6,392,209× 6,613,646× 6,506,686× 6,021,127× 6,403,218× 5,329,717× 4,990,345× 4,990,939× 4,615,046× 4,747,475× 4,846,497× 4,290,281× 3,936,095× 4,698,977× 5,186,814× 5,261,879× 4,959,516× 4,491,652× 4,772,462× 5,067,664× 5,021,158× 6,046,255× 4,972,471× 4,354,275× 3,008,003× 3,599,393× 4,044,906× 3,817,896× 3,968,159× 3,596,292× 3,557,142× 3,686,307× 3,115,425× 3,109,890× 3,005,766× 3,290,228× 2,247,414× 1,533,617× 1,825,816× 2,345,158× 2,442,506× 2,314,180× 1,700,244× 2,259,525× 3,244,318× 4,325,490× 4,323,242× 4,227,477× 3,724,714× 3,106,583× 2,935,240× 2,584,525× 3,110,352× 2,980,238× 2,887,787× 3,196,777× 3,455,412× 3,639,462× 3,506,370× 2,987,721× 2,844,376× 2,455,206× 2,622,670× 2,119,560× 1,569,738× 1,102,637× 1,085,106× 876,724× 1,138,837× 984,595× 988,137× 625,711× 427,782× 370,750× 604,958× 445,595× 313,358× 64,112× 4,236× 1,128× 1,146× | 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× 117,647× 1,143,112× 5,106,946× 14,484,662× 28,598,672× 48,480,384× 87,236,498× 120,937,690× 146,011,766× 164,233,178× 186,407,124× 203,014,930× 220,959,298× 254,058,288× 270,475,230× 340,775,510× 352,516,530× 398,067,788× 392,579,854× 390,859,748× 434,416,118× 392,041,810× 401,027,530× 363,075,920× 292,616,522× 272,678,984× 220,075,764× 210,844,278× 182,914,918× 175,883,062× 147,422,438× 103,815,282× 83,991,924× 94,404,580× 99,303,204× 76,290,924× 77,105,220× 77,511,252× 68,810,598× 62,146,318× 51,028,654× 30,900,058× 21,885,886× 7,409,120× 1,349,688× 343,316× 610,176× |