Base 118: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany calculation that has no results

Digits 1 2 3 4 5 6
Average Steps
Full Cycle		1.99 step
avg		21.38 step
avg		24.79 step
avg		31.83 step
avg		27.05 step
avg		287.13 step
avg
Step Frequency
Full Cycle
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1×
117×
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117×
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203×
642×
440×
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0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
24×
2,760×
2,832×
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0×
1×
3,657×
3,538×
7,074×
7,066×
7,054×
7,038×
7,018×
6,994×
6,966×
6,934×
6,898×
6,858×
6,814×
6,766×
6,714×
6,658×
6,598×
6,534×
6,466×
6,394×
6,318×
6,238×
6,154×
6,066×
5,974×
5,878×
5,778×
5,674×
5,566×
5,454×
5,338×
5,218×
5,094×
4,966×
4,834×
4,698×
4,558×
4,414×
4,266×
4,114×
3,958×
3,798×
3,634×
3,466×
3,294×
3,118×
2,938×
2,754×
2,566×
2,374×
2,178×
1,978×
1,774×
1,566×
1,354×
1,138×
918×
694×
466×
234×
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0×
1×
117×
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0×
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0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
519,680×
1,460,788×
5,844,776×
341,292×
301,979×
16,191×
10,586×
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0×
1×
117×
10,500×
195,066×
436,354×
352,498×
538,482×
964,272×
1,265,482×
1,845,494×
1,988,782×
2,815,122×
2,416,888×
3,847,930×
2,924,018×
5,105,906×
3,432,868×
6,438,894×
4,026,588×
7,829,550×
5,005,896×
9,301,906×
6,446,892×
10,508,544×
7,873,754×
11,046,354×
8,403,260×
10,826,544×
7,852,778×
10,344,830×
7,229,384×
9,637,206×
6,563,956×
8,615,598×
5,982,626×
7,088,448×
5,369,582×
5,553,520×
4,100,406×
4,006,122×
2,864,938×
2,377,236×
1,604,888×
1,080,282×
654,338×
323,632×
135,070×
50,114×
5,088×
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0×
1×
44,117×
66,470×
0×
122,108×
323,694×
0×
0×
0×
0×
0×
0×
0×
0×
90,181×
303,353×
457,696×
566,248×
596,174×
753,750×
264,726×
372,196×
372,846×
147,410×
98,656×
176,744×
119,801×
147,909×
136,454×
115,570×
415,556×
871,519×
975,736×
1,272,796×
1,112,060×
1,435,012×
1,505,093×
1,597,440×
1,539,039×
1,390,260×
1,336,013×
1,180,793×
1,451,924×
1,551,893×
1,785,402×
1,943,503×
1,719,025×
1,050,392×
2,460,970×
3,925,001×
2,845,737×
3,270,457×
3,096,006×
3,499,602×
3,842,502×
4,165,281×
3,849,276×
3,227,375×
3,518,968×
3,499,554×
5,233,700×
4,437,654×
4,724,317×
4,936,556×
4,973,458×
5,236,107×
5,726,453×
4,536,483×
4,267,401×
3,666,672×
3,669,863×
3,647,283×
3,919,600×
3,460,878×
4,014,960×
4,391,420×
3,997,755×
4,973,664×
5,173,647×
4,879,976×
5,291,307×
5,077,467×
4,939,646×
5,886,811×
6,632,772×
6,322,006×
6,162,649×
5,423,524×
5,688,051×
5,624,662×
6,182,725×
5,172,847×
5,841,826×
5,795,209×
5,036,915×
5,005,381×
5,550,656×
5,742,757×
5,555,672×
6,922,645×
6,972,263×
5,194,890×
5,060,234×
6,272,475×
5,912,052×
5,829,474×
7,326,019×
6,581,471×
5,898,820×
6,164,957×
6,555,282×
6,292,813×
6,347,797×
6,166,872×
6,201,218×
5,669,240×
5,244,101×
5,937,602×
4,918,781×
5,291,932×
5,594,490×
6,207,139×
5,558,437×
5,088,152×
4,901,745×
4,518,337×
4,613,958×
4,498,933×
3,722,837×
3,373,374×
3,410,897×
3,273,155×
3,126,121×
2,811,151×
2,919,453×
3,060,033×
2,563,510×
2,013,903×
2,358,392×
1,912,217×
1,441,798×
1,269,150×
1,034,999×
944,922×
1,007,842×
1,139,600×
732,164×
643,142×
789,315×
954,765×
1,113,999×
1,834,065×
1,768,508×
2,121,039×
2,107,841×
2,279,866×
2,039,132×
2,405,385×
2,554,991×
3,213,405×
3,474,404×
2,774,948×
2,279,950×
1,783,996×
1,711,256×
1,880,018×
1,814,511×
2,392,245×
1,932,672×
2,345,216×
2,375,182×
2,379,243×
2,881,101×
2,385,424×
2,901,676×
3,001,902×
2,775,426×
2,046,503×
1,934,160×
2,168,392×
2,288,281×
2,024,346×
1,892,800×
1,868,946×
1,857,705×
1,415,989×
1,189,868×
1,513,432×
4,471,298×
8,923,679×
8,301,761×
10,490,843×
13,421,518×
12,265,951×
13,099,457×
14,136,632×
14,141,410×
13,603,261×
13,415,944×
13,140,463×
11,673,990×
12,056,665×
12,549,929×
12,918,037×
13,121,201×
13,436,267×
14,516,253×
13,601,163×
12,850,283×
15,903,522×
15,858,729×
15,591,753×
14,874,181×
15,223,286×
16,692,244×
16,013,358×
15,880,086×
14,861,328×
15,439,527×
14,912,546×
15,717,603×
17,008,654×
16,656,543×
17,884,156×
18,209,246×
18,342,790×
17,398,666×
17,419,269×
17,728,674×
16,703,615×
16,094,454×
15,958,996×
14,741,922×
14,488,641×
14,215,555×
14,166,036×
15,463,966×
15,999,019×
15,244,925×
17,153,250×
17,990,089×
17,215,157×
15,386,432×
15,231,359×
15,199,108×
14,143,204×
14,402,900×
15,604,812×
15,369,304×
15,710,921×
16,183,071×
17,291,212×
16,835,806×
16,178,955×
17,998,657×
15,581,628×
15,229,254×
15,733,282×
15,377,853×
16,583,812×
16,511,187×
17,001,372×
17,850,131×
17,084,117×
16,799,364×
17,490,347×
17,522,252×
18,344,342×
18,177,535×
17,518,242×
17,246,281×
17,466,986×
18,309,029×
17,948,116×
17,596,452×
16,946,788×
16,763,768×
16,448,850×
16,891,817×
17,495,789×
17,558,471×
17,064,556×
15,348,082×
17,063,703×
17,786,192×
19,226,442×
18,924,454×
18,192,543×
18,740,274×
19,738,808×
18,533,377×
16,408,320×
16,530,838×
15,789,900×
17,661,226×
18,176,374×
18,707,954×
21,134,885×
21,254,568×
20,419,122×
21,304,921×
21,737,261×
20,437,984×
19,810,059×
18,432,634×
18,500,188×
18,062,781×
15,457,169×
15,446,533×
16,714,481×
16,905,865×
15,924,953×
13,898,862×
15,183,155×
14,879,646×
13,196,153×
13,793,403×
13,108,196×
12,308,211×
11,035,512×
12,662,827×
13,408,939×
12,896,483×
13,645,439×
12,602,899×
11,735,505×
10,965,499×
12,988,131×
12,670,991×
12,207,905×
11,458,023×
9,848,849×
9,404,396×
9,315,805×
9,552,965×
10,329,182×
8,441,890×
8,229,149×
7,400,419×
7,233,573×
7,239,218×
8,068,868×
7,866,250×
6,406,419×
6,268,824×
7,346,185×
6,340,329×
5,208,979×
5,967,544×
4,875,350×
5,328,784×
6,843,950×
5,418,361×
5,031,984×
5,046,565×
5,346,077×
6,611,607×
7,691,207×
7,741,497×
7,817,647×
8,417,384×
9,748,904×
12,261,034×
13,716,430×
12,188,059×
12,023,103×
11,844,953×
12,942,710×
13,957,323×
13,468,963×
13,657,257×
12,449,522×
12,056,445×
10,841,309×
11,900,803×
11,890,486×
12,276,104×
13,143,412×
13,029,825×
11,975,988×
13,268,311×
14,290,314×
14,726,128×
16,017,421×
16,296,338×
16,014,153×
17,680,423×
18,252,968×
17,686,601×
18,960,509×
18,736,555×
18,782,144×
17,271,151×
17,159,370×
16,665,636×
17,186,468×
16,455,069×
16,295,496×
16,224,376×
15,891,131×
16,499,295×
16,075,368×
17,376,745×
14,447,321×
13,768,177×
12,098,766×
12,916,575×
13,306,978×
12,453,764×
12,860,864×
14,518,934×
13,692,022×
12,816,465×
13,624,752×
12,348,812×
12,885,390×
10,821,442×
10,778,092×
10,752,481×
11,554,955×
11,763,575×
11,560,382×
10,028,143×
9,648,792×
9,735,652×
9,816,174×
9,734,262×
9,698,218×
9,381,620×
10,198,101×
10,401,803×
9,328,480×
9,465,404×
9,977,947×
8,897,439×
9,750,819×
9,664,369×
9,907,284×
8,831,030×
8,735,362×
7,597,302×
8,115,761×
8,837,410×
9,214,903×
8,336,058×
6,696,390×
6,561,620×
6,510,002×
6,970,624×
5,577,224×
5,574,519×
5,127,862×
5,837,383×
5,256,600×
4,818,608×
4,777,280×
4,209,697×
4,529,254×
5,158,245×
4,699,451×
4,270,085×
4,798,315×
3,716,049×
4,003,275×
4,572,123×
3,858,221×
3,400,535×
2,754,995×
2,972,536×
2,506,345×
2,663,089×
2,506,932×
2,036,508×
2,748,373×
2,329,869×
1,977,191×
1,812,297×
2,048,672×
1,765,689×
1,722,458×
1,965,224×
1,253,489×
1,277,332×
944,146×
565,461×
457,136×
674,725×
376,057×
118,205×
152,376×
89,144×