| 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 |
| 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 |
|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.98 step avg | 1.47 step avg | 14.01 step avg | 2.94 step avg | 15.99 step avg | 51.18 step avg | 17.93 step avg | 55.17 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 65× | 0s: 1s: 2s: 18× 1,137× 1,056× | 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× 1,187× 1,120× 2,238× 2,230× 2,218× 2,202× 2,182× 2,158× 2,130× 2,098× 2,062× 2,022× 1,978× 1,930× 1,878× 1,822× 1,762× 1,698× 1,630× 1,558× 1,482× 1,402× 1,318× 1,230× 1,138× 1,042× 942× 838× 730× 618× 502× 382× 258× 130× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 1× 51,745× 138,480× 554,400× 59,335× 51,395× 5,193× 3,952× | 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: 1× 15,001× 18,286× 28,546× 62,826× 103,246× 180,680× 226,074× 334,982× 306,454× 576,342× 619,540× 795,286× 729,302× 919,236× 718,750× 933,674× 764,716× 869,160× 695,054× 696,634× 543,648× 538,738× 411,562× 332,264× 256,394× 200,064× 137,810× 66,260× 20,244× 2,240× | 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: 1× 419,322× 844,565× 1,082,274× 857,297× 1,055,948× 1,088,024× 1,407,990× 1,472,836× 1,429,774× 1,616,184× 1,575,244× 1,426,114× 1,588,691× 1,727,721× 2,080,622× 2,019,123× 1,844,497× 2,048,005× 2,046,570× 2,055,809× 2,131,940× 2,137,762× 2,438,116× 2,249,577× 2,443,995× 2,138,599× 2,116,961× 1,806,716× 1,708,610× 1,763,600× 1,572,799× 1,451,270× 1,574,400× 1,470,293× 1,742,721× 1,479,731× 1,406,412× 1,670,650× 1,787,350× 1,517,274× 1,417,413× 1,245,028× 1,353,876× 1,196,225× 1,340,317× 1,435,696× 1,715,216× 1,589,049× 1,425,418× 1,283,945× 1,315,263× 1,271,275× 1,385,690× 1,416,801× 1,484,144× 1,302,285× 1,224,608× 1,156,739× 1,236,373× 1,203,158× 1,141,245× 1,419,270× 1,509,206× 1,262,238× 1,025,623× 1,195,223× 1,183,400× 1,422,227× 1,471,004× 1,327,795× 1,261,792× 924,457× 851,520× 949,794× 740,776× 713,699× 831,036× 842,732× 968,834× 1,198,935× 1,135,923× 946,329× 990,272× 878,164× 921,556× 925,986× 886,310× 1,049,773× 851,043× 662,817× 648,118× 514,785× 503,236× 494,786× 442,570× 454,272× 548,920× 497,845× 453,507× 469,605× 427,149× 422,344× 446,729× 315,646× 258,282× 291,032× 320,808× 290,873× 278,401× 372,708× 346,703× 365,617× 284,533× 274,436× 358,778× 312,659× 382,899× 382,348× 219,716× 177,837× 122,574× 95,994× 113,664× 155,395× 177,780× 144,071× 68,740× 62,308× 49,920× 80,677× 132,470× 161,559× 186,873× 274,681× 170,132× 146,779× 160,794× 196,653× 265,385× 249,646× 184,948× 213,290× 274,949× 157,568× 133,768× 116,756× 175,402× 162,617× 173,125× 163,534× 125,466× 137,940× 99,868× 137,352× 146,761× 178,280× 115,651× 150,094× 205,490× 133,060× 114,752× 113,062× 82,890× 127,972× 82,198× 13,900× 22,912× 20,110× 22,726× 20,696× 20,400× 35,340× | 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: 1× 349,483× 916,094× 2,309,688× 2,907,056× 4,713,102× 7,550,432× 11,474,934× 15,611,732× 23,565,780× 33,162,924× 41,635,306× 52,953,434× 67,385,336× 77,291,708× 83,197,910× 103,405,016× 116,266,580× 119,882,448× 123,197,096× 125,885,362× 111,813,262× 99,032,716× 85,048,168× 63,974,180× 39,273,164× 26,534,646× 17,799,236× 8,625,500× 4,040,134× 2,274,032× 880,476× 123,682× 29,086× | 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: 1× 6,455,356× 26,676,726× 19,170,259× 27,736,410× 30,924,332× 34,593,813× 39,852,179× 53,526,501× 53,288,825× 63,620,300× 71,017,514× 81,710,951× 90,205,737× 100,669,182× 97,843,148× 110,703,900× 113,484,224× 116,618,172× 122,572,832× 131,884,668× 129,111,741× 127,985,754× 134,707,477× 136,947,374× 152,236,846× 148,083,381× 146,817,738× 149,974,467× 147,032,301× 156,896,272× 168,384,009× 155,708,873× 155,925,179× 155,807,934× 156,078,301× 154,371,918× 167,995,174× 161,537,651× 168,269,454× 160,238,259× 169,648,646× 163,135,713× 170,929,636× 171,352,131× 181,244,565× 192,305,844× 187,634,924× 185,132,225× 184,988,673× 176,565,310× 179,586,860× 182,464,060× 205,915,297× 200,582,317× 193,298,076× 179,648,753× 192,033,728× 174,701,508× 187,575,295× 174,535,945× 172,360,948× 169,156,368× 171,645,522× 175,583,908× 182,588,664× 176,616,302× 181,931,600× 176,352,076× 168,136,726× 152,314,601× 145,052,844× 138,455,911× 123,323,071× 110,445,487× 115,080,504× 107,291,642× 107,664,066× 104,060,469× 97,335,492× 102,937,143× 108,695,612× 106,078,804× 105,290,114× 97,041,476× 94,593,814× 95,075,837× 87,954,717× 86,444,726× 87,704,808× 86,370,727× 77,003,152× 68,319,939× 68,901,702× 66,315,434× 65,907,387× 65,780,843× 63,285,123× 57,994,486× 55,681,666× 51,370,149× 47,716,589× 47,658,484× 51,175,662× 44,586,914× 42,387,995× 36,294,549× 40,206,684× 38,433,878× 39,169,077× 30,998,866× 29,398,115× 28,621,502× 25,903,357× 24,302,255× 20,126,462× 21,238,878× 21,113,892× 20,519,231× 19,016,724× 15,020,599× 13,100,703× 11,132,778× 12,582,280× 15,140,704× 16,808,130× 14,253,302× 13,364,069× 13,299,049× 13,554,095× 11,219,051× 13,565,371× 9,235,828× 8,971,995× 8,973,122× 9,041,112× 8,015,063× 6,860,495× 5,529,803× 5,387,840× 5,611,252× 6,647,190× 5,645,135× 3,018,253× 2,601,425× 2,421,885× 1,592,360× 1,242,080× 476,436× 362,592× 94,406× 109,474× 83,803× 197,044× 249,350× 85,788× 269,546× 286,542× 693,914× 1,204,060× 1,036,160× 184,352× |