| 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 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Average Steps Cycle Start | 0.98 step avg | 2.17 step avg | 8.79 step avg | 1.84 step avg | 9.57 step avg | 19.25 step avg | 13.40 step avg | 23.66 step avg | 18.39 step avg | 42.76 step avg |
| Step Frequency Cycle Start | 0s: 1s: 1× 40× | 0s: 1s: 2s: 3s: 6× 245× 210× 400× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 20s: 21s: 1× 921× 437× 872× 862× 848× 830× 808× 782× 752× 718× 680× 638× 592× 542× 488× 430× 368× 302× 232× 158× 80× | 0s: 1s: 2s: 3s: 4s: 1× 31,960× 93,730× 9,620× 440× | 0s: 1s: 2s: 3s: 4s: 5s: 6s: 7s: 8s: 9s: 10s: 11s: 12s: 13s: 14s: 15s: 16s: 17s: 18s: 19s: 1× 11,744× 17,166× 19,592× 45,268× 63,413× 89,133× 119,634× 138,423× 114,517× 126,545× 116,505× 97,889× 86,887× 56,984× 39,671× 26,442× 26,822× 18,899× 6,224× | 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: 1× 89,684× 236,513× 505,490× 383,882× 422,672× 273,217× 234,557× 256,116× 239,410× 253,960× 339,241× 280,266× 288,156× 331,970× 330,842× 273,091× 289,528× 294,129× 209,376× 204,682× 186,678× 197,563× 178,926× 174,837× 160,500× 151,009× 134,038× 177,194× 150,687× 120,716× 121,620× 108,419× 135,259× 162,268× 173,832× 114,580× 91,494× 64,217× 72,411× 81,797× 89,610× 80,495× 85,658× 42,979× 70,006× 76,165× 73,394× 46,984× 55,160× 36,721× 50,702× 49,686× 30,285× 16,352× 15,413× 15,227× 8,780× 13,371× 7,678× 5,269× 2,056× | 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: 1× 113,660× 254,656× 596,679× 1,003,397× 1,656,316× 2,198,171× 3,028,570× 3,984,750× 4,643,146× 4,988,561× 5,124,085× 4,342,533× 4,333,751× 3,200,776× 2,778,214× 2,023,447× 2,177,826× 2,040,089× 2,610,835× 2,597,485× 2,549,409× 1,964,433× 1,650,448× 1,256,871× 732,073× 549,883× 368,587× 110,684× 11,861× 302× | 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: 1× 196,065× 687,067× 3,568,045× 4,859,659× 9,456,885× 7,936,874× 7,495,313× 6,795,897× 7,259,872× 7,054,712× 7,816,624× 8,842,922× 9,014,502× 8,981,892× 9,086,470× 8,286,087× 8,881,576× 9,206,512× 11,261,590× 11,867,248× 10,424,858× 10,791,675× 8,802,000× 11,406,318× 15,721,383× 14,288,542× 12,630,385× 12,080,961× 12,613,929× 8,923,761× 9,495,060× 8,947,238× 11,231,106× 11,123,658× 11,464,081× 9,563,304× 8,463,971× 7,214,382× 5,706,525× 5,738,656× 4,974,768× 4,285,857× 3,960,820× 3,309,354× 1,857,091× 1,257,715× 990,140× 729,971× 350,245× 213,720× 139,287× 73,233× 12,001× 7,186× | 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: 1× 1,052,504× 4,762,755× 11,593,163× 22,144,871× 38,627,330× 52,234,226× 66,651,433× 66,957,983× 71,316,077× 71,924,944× 75,682,342× 78,356,006× 78,162,145× 91,854,927× 102,923,262× 117,828,945× 120,755,800× 109,122,048× 90,618,964× 69,423,022× 63,490,835× 41,874,564× 35,649,269× 36,275,604× 55,977,653× 58,540,725× 58,818,658× 48,391,560× 34,776,774× 31,231,693× 33,350,499× 46,381,267× 44,899,196× 44,941,524× 27,345,786× 16,865,189× 9,971,204× 8,863,517× 5,328,910× 3,146,460× 3,910,508× 1,842,270× 573,453× 15,768× | 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: 1× 584,757× 4,615,350× 31,228,538× 83,197,235× 242,614,919× 194,912,154× 148,176,519× 145,561,583× 206,777,315× 180,581,329× 145,972,865× 149,657,818× 192,529,415× 183,306,051× 156,781,700× 176,888,598× 157,020,589× 176,721,948× 158,253,884× 184,567,021× 173,390,510× 131,428,260× 113,265,034× 115,559,422× 149,130,511× 167,472,636× 166,178,198× 125,423,021× 103,225,519× 88,200,200× 92,597,304× 88,370,581× 106,205,559× 69,019,209× 101,361,319× 95,091,177× 88,534,652× 58,569,273× 45,554,357× 64,681,072× 72,238,975× 91,027,304× 62,891,234× 66,851,964× 63,805,331× 72,022,668× 87,911,788× 70,581,771× 92,107,327× 76,218,711× 67,515,270× 51,196,311× 70,955,004× 64,258,424× 95,618,562× 135,226,676× 135,941,016× 100,588,387× 120,492,612× 112,402,796× 126,247,728× 148,861,681× 222,206,309× 160,944,549× 169,284,600× 218,061,386× 247,825,082× 205,509,581× 205,751,015× 195,169,341× 155,295,503× 145,153,234× 99,216,545× 78,053,223× 82,965,107× 69,357,624× 75,951,877× 62,224,863× 43,538,269× 42,340,128× 76,685,016× 66,616,609× 57,141,463× 57,452,703× 53,363,094× 39,536,825× 32,970,487× 39,208,595× 52,392,356× 32,947,778× 47,063,791× 41,841,292× 29,497,608× 30,801,258× 13,252,362× 7,196,862× 9,924,190× 12,378,060× 6,146,462× 7,987,417× 5,153,898× 4,060,625× 3,598,565× 4,533,201× 2,877,967× 3,563,671× 1,030,159× 775,458× 1,724,369× 1,179,984× 609,228× 337,584× 1,412,054× |