| 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 |
| Γ | Δ | Ε | Ζ | Η | Θ | Ι | Κ | Λ | Μ | Ν | Ξ | Ο | Π | Ρ | Σ |
| Τ | Υ | Φ | Χ | Ψ | Ω | α | β | γ | δ | ε | ζ | η | θ | ι | κ |
| λ | μ | ν | ξ | ο | π | ρ | ς | σ | τ | υ | φ | χ | ψ | ω | А |
| Б | В | Г | Д | Е | Ж | З | И | Й | К | Л | М | Н | О | П | Р |
| 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 |
|---|---|---|---|---|---|---|
| Average Steps Full Cycle | 1.99 step avg | 12.04 step avg | 24.41 step avg | 17.54 step avg | 26.44 step avg | 279.75 step avg |
| Step Frequency Full Cycle | 0s: 1s: 2s: 0× 1× 115× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 0× 2× 191× 39× 178× 166× 3× 369× 318× 0× 0× 0× 24× 2,712× 2,784× | 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: 0× 1× 3,537× 3,420× 6,838× 6,830× 6,818× 6,802× 6,782× 6,758× 6,730× 6,698× 6,662× 6,622× 6,578× 6,530× 6,478× 6,422× 6,362× 6,298× 6,230× 6,158× 6,082× 6,002× 5,918× 5,830× 5,738× 5,642× 5,542× 5,438× 5,330× 5,218× 5,102× 4,982× 4,858× 4,730× 4,598× 4,462× 4,322× 4,178× 4,030× 3,878× 3,722× 3,562× 3,398× 3,230× 3,058× 2,882× 2,702× 2,518× 2,330× 2,138× 1,942× 1,742× 1,538× 1,330× 1,118× 902× 682× 458× 230× | 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× 115× 0× 0× 0× 0× 0× 8,664× 24,908× 97,440× 389,760× 23,720× 22,054× 38,774× 111,456× 291,408× 1,169,280× 4,677,120× 282,040× 250,369× 465,402× 28,034× 22,012× 38,194× | 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: 0× 1× 115× 10,148× 3,422× 243,204× 254,416× 350,942× 768,668× 1,086,660× 1,680,754× 1,865,998× 2,717,852× 2,367,142× 4,090,282× 3,389,142× 5,341,080× 3,886,668× 6,596,048× 4,413,356× 7,878,784× 5,645,564× 9,359,054× 7,539,994× 10,196,084× 8,074,324× 9,849,060× 7,629,638× 9,172,962× 6,954,698× 8,936,814× 6,290,318× 7,815,726× 5,884,960× 6,486,032× 5,222,080× 5,265,156× 4,358,282× 4,067,792× 3,466,378× 2,962,966× 2,505,266× 1,953,330× 1,476,976× 967,758× 678,154× 460,400× 280,202× 126,536× 6,838× | 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: 362s: 363s: 364s: 365s: 366s: 367s: 368s: 369s: 370s: 371s: 372s: 373s: 374s: 375s: 376s: 377s: 378s: 379s: 380s: 381s: 382s: 383s: 384s: 385s: 386s: 387s: 388s: 389s: 390s: 391s: 392s: 393s: 394s: 395s: 396s: 397s: 398s: 399s: 400s: 401s: 402s: 403s: 404s: 405s: 406s: 407s: 408s: 409s: 410s: 411s: 412s: 413s: 414s: 415s: 416s: 417s: 418s: 419s: 420s: 421s: 422s: 423s: 424s: 425s: 426s: 427s: 428s: 429s: 430s: 431s: 432s: 433s: 434s: 435s: 436s: 437s: 438s: 439s: 440s: 441s: 442s: 443s: 444s: 445s: 446s: 447s: 448s: 449s: 450s: 451s: 452s: 453s: 454s: 455s: 456s: 457s: 458s: 459s: 460s: 461s: 462s: 463s: 464s: 465s: 466s: 467s: 468s: 469s: 470s: 471s: 472s: 473s: 474s: 475s: 476s: 477s: 478s: 479s: 480s: 481s: 482s: 483s: 484s: 485s: 486s: 487s: 488s: 489s: 490s: 491s: 492s: 493s: 494s: 495s: 496s: 497s: 498s: 499s: 500s: 501s: 502s: 503s: 504s: 505s: 506s: 507s: 508s: 509s: 510s: 511s: 512s: 513s: 514s: 515s: 516s: 517s: 518s: 519s: 520s: 521s: 522s: 523s: 524s: 525s: 526s: 527s: 528s: 529s: 530s: 531s: 532s: 533s: 534s: 535s: 536s: 537s: 538s: 539s: 540s: 541s: 542s: 543s: 544s: 545s: 546s: 547s: 548s: 549s: 550s: 551s: 552s: 553s: 554s: 555s: 556s: 557s: 558s: 559s: 560s: 561s: 562s: 563s: 564s: 565s: 566s: 567s: 568s: 569s: 570s: 571s: 572s: 573s: 574s: 575s: 576s: 577s: 578s: 579s: 580s: 581s: 582s: 583s: 584s: 585s: 586s: 587s: 588s: 589s: 590s: 591s: 592s: 593s: 594s: 595s: 596s: 597s: 598s: 599s: 600s: 601s: 602s: 603s: 604s: 605s: 606s: 607s: 608s: 609s: 610s: 611s: 612s: 613s: 614s: 615s: 616s: 617s: 618s: 619s: 620s: 621s: 622s: 623s: 624s: 625s: 626s: 627s: 628s: 629s: 630s: 631s: 632s: 633s: 634s: 635s: 636s: 637s: 638s: 639s: 640s: 641s: 642s: 643s: 644s: 645s: 646s: 647s: 648s: 649s: 650s: 651s: 652s: 653s: 654s: 0× 1× 40,041× 78,754× 146,084× 338,042× 97,616× 238,838× 606,348× 115,812× 259,046× 244,094× 368,064× 968,312× 3,013,206× 1,597,304× 1,165,208× 1,445,342× 1,689,810× 1,970,502× 2,291,332× 2,540,654× 2,613,600× 3,158,014× 3,063,296× 4,140,725× 4,669,922× 7,192,909× 8,290,085× 10,168,198× 9,760,371× 9,582,880× 7,538,793× 7,869,832× 7,906,470× 9,271,342× 10,234,225× 11,164,437× 10,897,302× 13,295,361× 13,255,625× 11,995,400× 14,220,866× 12,948,811× 11,137,980× 12,009,801× 10,699,058× 9,508,359× 9,801,771× 10,363,060× 9,957,804× 10,608,177× 10,644,531× 9,223,048× 9,286,586× 7,989,991× 7,589,194× 6,170,152× 6,252,332× 6,340,508× 4,310,232× 4,402,022× 4,449,902× 3,362,973× 3,690,156× 3,955,918× 4,849,627× 4,816,204× 4,602,754× 4,544,454× 4,690,112× 5,917,561× 6,631,237× 7,312,576× 6,574,786× 6,696,868× 5,323,233× 5,560,640× 6,157,262× 5,876,336× 6,789,777× 7,502,764× 7,631,549× 7,839,237× 7,903,537× 7,454,040× 7,323,945× 7,569,154× 8,362,127× 8,171,080× 6,333,824× 7,391,873× 7,042,911× 6,098,678× 6,202,591× 6,686,715× 6,611,532× 6,386,362× 7,099,774× 6,580,940× 6,024,308× 5,269,943× 4,572,590× 3,875,678× 4,218,492× 5,221,350× 6,330,110× 5,604,955× 5,838,950× 7,993,149× 9,534,355× 9,630,243× 10,906,169× 14,459,111× 15,867,736× 15,598,019× 15,762,911× 16,139,613× 17,850,437× 17,128,444× 15,128,184× 14,804,929× 14,789,842× 15,139,843× 15,690,649× 15,245,958× 15,054,994× 12,226,492× 13,589,393× 10,949,653× 11,112,098× 9,689,214× 10,821,337× 11,300,734× 9,482,947× 9,795,003× 10,062,743× 10,071,058× 9,439,256× 9,679,961× 8,714,886× 8,699,007× 7,198,744× 5,994,317× 6,473,081× 5,186,506× 5,097,790× 5,599,060× 5,429,707× 6,276,435× 6,591,134× 6,504,285× 6,636,315× 8,065,869× 7,068,180× 6,749,290× 5,723,477× 6,385,732× 7,287,076× 7,158,195× 6,238,038× 6,075,479× 6,205,802× 6,019,628× 6,398,733× 4,816,552× 4,278,926× 3,912,997× 3,205,932× 2,624,066× 2,567,286× 2,235,632× 2,477,966× 2,373,534× 3,453,421× 4,203,867× 4,105,816× 4,267,732× 4,608,506× 4,911,630× 5,897,929× 6,503,300× 5,869,657× 6,428,110× 7,571,820× 8,325,531× 9,866,912× 10,103,143× 9,904,762× 9,216,221× 10,704,422× 10,236,639× 10,196,019× 9,512,101× 8,575,763× 9,653,367× 10,024,838× 8,811,842× 9,460,148× 10,615,067× 10,200,345× 8,638,650× 8,780,315× 8,852,577× 7,269,931× 7,841,724× 7,270,748× 8,059,640× 6,947,365× 6,836,167× 5,774,227× 4,754,112× 4,898,637× 5,366,898× 5,486,932× 5,618,176× 5,142,443× 5,252,632× 4,600,723× 4,340,749× 4,776,400× 3,933,880× 3,604,664× 3,660,324× 2,553,308× 3,113,840× 3,063,429× 2,937,514× 3,768,148× 2,937,262× 3,113,684× 3,006,723× 3,548,237× 3,522,814× 3,349,987× 3,457,194× 4,361,928× 5,030,813× 6,215,019× 5,832,546× 5,457,676× 4,142,923× 5,217,668× 5,059,708× 4,427,511× 4,676,282× 4,803,771× 4,959,612× 5,232,539× 4,835,568× 5,159,340× 4,813,931× 4,575,644× 5,343,528× 5,181,272× 5,327,560× 5,348,878× 3,680,858× 3,284,470× 3,336,150× 3,490,506× 3,026,076× 3,268,952× 4,320,289× 3,592,639× 3,299,314× 4,123,518× 4,474,313× 4,820,214× 3,478,968× 2,828,354× 2,605,541× 2,986,518× 3,260,944× 2,520,836× 2,469,827× 2,744,094× 2,782,754× 3,009,774× 3,335,498× 3,041,124× 2,708,466× 2,906,343× 2,854,046× 2,408,685× 2,378,291× 2,638,059× 3,093,727× 2,634,333× 2,005,740× 2,295,840× 1,806,882× 1,961,260× 2,204,356× 2,322,018× 2,274,126× 2,464,050× 2,493,194× 2,790,878× 3,018,004× 2,590,114× 3,297,236× 3,680,980× 3,492,210× 4,566,114× 6,159,837× 5,675,006× 5,784,456× 5,971,779× 7,604,166× 6,492,653× 7,537,850× 7,439,561× 7,487,484× 8,792,821× 9,024,228× 9,249,327× 10,957,607× 10,426,567× 11,338,064× 9,901,774× 10,475,810× 10,373,262× 9,404,655× 10,523,406× 9,844,189× 9,362,765× 9,696,668× 11,262,409× 11,792,842× 11,734,426× 10,703,015× 11,827,830× 11,015,531× 10,891,837× 11,120,119× 11,614,610× 12,480,828× 11,323,129× 11,138,091× 12,456,867× 12,407,557× 12,558,939× 11,284,822× 12,901,210× 11,985,607× 10,921,381× 11,528,854× 10,659,112× 11,083,676× 11,505,746× 11,882,505× 12,119,835× 11,772,840× 13,698,778× 13,568,416× 13,125,884× 13,491,010× 12,432,687× 12,900,581× 11,779,376× 12,257,046× 12,283,639× 13,198,551× 13,915,487× 14,261,977× 14,227,388× 13,327,183× 13,288,326× 12,656,051× 12,652,652× 11,945,831× 11,672,766× 11,386,587× 10,463,526× 11,460,405× 11,259,942× 11,352,367× 11,990,572× 11,226,972× 10,530,128× 11,725,459× 13,073,007× 14,749,605× 14,278,257× 14,059,823× 12,418,552× 12,428,850× 14,195,456× 12,484,862× 14,776,822× 14,338,459× 12,567,116× 12,504,292× 12,023,329× 11,309,375× 11,626,057× 11,139,295× 10,863,352× 10,232,091× 11,869,709× 11,339,320× 10,799,247× 12,656,392× 11,965,378× 11,416,282× 12,381,873× 12,739,992× 13,045,272× 11,592,556× 11,368,357× 9,055,748× 8,213,081× 9,269,649× 9,220,861× 9,840,625× 8,733,306× 8,216,161× 7,993,663× 7,957,423× 8,642,309× 8,339,481× 7,553,210× 6,780,520× 7,154,652× 7,259,853× 6,093,818× 6,960,743× 5,403,211× 5,580,290× 5,214,598× 4,102,652× 5,000,510× 4,378,216× 3,998,013× 3,884,224× 4,003,250× 3,956,770× 4,624,874× 3,458,650× 3,374,800× 3,716,736× 3,670,743× 4,477,134× 4,516,514× 4,051,271× 3,765,328× 4,246,322× 4,587,742× 3,958,860× 3,450,588× 4,504,941× 4,681,415× 5,176,518× 4,096,288× 3,548,515× 3,528,427× 4,243,043× 3,820,698× 4,286,373× 3,821,167× 3,663,336× 3,831,165× 3,955,160× 3,327,744× 3,682,423× 2,456,439× 2,141,756× 2,938,006× 1,790,032× 1,707,420× 1,263,014× 1,283,968× 1,197,872× 1,313,164× 1,735,533× 1,727,440× 2,156,118× 1,960,230× 2,549,066× 2,034,533× 2,233,341× 2,080,827× 2,146,704× 2,610,086× 2,910,636× 2,194,916× 2,775,972× 2,192,070× 2,389,866× 2,652,204× 2,050,891× 1,944,069× 1,399,470× 1,746,756× 2,225,656× 2,419,416× 2,344,393× 2,274,550× 2,131,949× 2,958,112× 3,131,558× 4,231,199× 2,807,232× 3,241,216× 3,625,393× 4,004,431× 3,902,496× 4,494,784× 4,083,221× 3,601,448× 4,473,066× 3,806,906× 3,207,710× 3,408,290× 2,984,364× 3,773,635× 3,148,158× 3,701,093× 3,937,935× 3,873,232× 3,877,171× 4,799,811× 5,245,733× 4,240,375× 3,952,282× 3,095,380× 4,680,454× 4,640,304× 5,382,526× 5,531,743× 5,622,852× 5,902,358× 6,286,646× 6,147,248× 6,019,948× 6,924,818× 5,696,923× 5,915,946× 5,216,451× 4,753,766× 3,561,536× 3,745,390× 4,921,332× 3,862,872× 3,581,130× 3,398,402× 2,986,985× 3,670,521× 3,373,670× 4,081,142× 3,367,016× 3,026,963× 2,647,980× 2,619,203× 2,837,879× 3,545,458× 3,850,360× 3,465,750× 2,400,072× 2,485,458× 2,041,645× 1,517,206× 1,905,560× 1,687,806× 1,644,839× 1,174,734× 1,251,416× 1,449,483× 1,611,730× 1,308,908× 1,294,290× 1,607,438× 1,466,756× 1,782,202× 2,159,142× 1,860,148× 2,171,446× 2,405,684× 3,002,786× 2,845,978× 3,104,109× 2,273,925× 2,819,018× 2,224,832× 2,054,206× 2,928,892× 1,977,440× 2,283,359× 2,195,079× 2,076,190× 2,624,769× 1,801,492× 1,921,716× 2,246,010× 2,365,719× 2,503,200× 1,887,044× 1,899,510× 1,908,448× 1,773,999× 2,214,884× 1,938,331× 2,025,138× 1,379,231× 1,556,348× 1,783,146× 1,195,284× 1,450,242× 1,019,188× 919,344× 853,578× 1,044,332× 1,248,824× 983,100× 765,624× 1,039,058× 1,201,859× 889,568× 1,183,827× 1,014,409× 1,872,638× 1,681,176× 1,756,448× 1,878,342× 974,202× 1,341,946× 1,531,842× 1,273,348× 1,432,246× 1,634,562× 1,447,736× 1,276,474× 1,168,618× 1,317,302× 969,696× 784,842× 901,794× 745,578× 898,229× 647,502× 355,348× 373,028× 604,676× 370,006× 477,160× 631,172× 712,225× 504,524× 659,416× 705,948× 668,024× 279,928× 294,228× 68,226× |