Base 124: 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		42.83 step
avg		25.91 step
avg		9.04 step
avg		28.16 step
avg		302.40 step
avg
Step Frequency
Full Cycle
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1×
123×
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124×
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615×
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25×
3,051×
3,074×
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0×
1×
4,029×
3,904×
7,806×
7,798×
7,786×
7,770×
7,750×
7,726×
7,698×
7,666×
7,630×
7,590×
7,546×
7,498×
7,446×
7,390×
7,330×
7,266×
7,198×
7,126×
7,050×
6,970×
6,886×
6,798×
6,706×
6,610×
6,510×
6,406×
6,298×
6,186×
6,070×
5,950×
5,826×
5,698×
5,566×
5,430×
5,290×
5,146×
4,998×
4,846×
4,690×
4,530×
4,366×
4,198×
4,026×
3,850×
3,670×
3,486×
3,298×
3,106×
2,910×
2,710×
2,506×
2,298×
2,086×
1,870×
1,650×
1,426×
1,198×
966×
730×
490×
246×
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0×
1×
123×
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0×
156,800×
416,220×
1,666,560×
6,666,240×
375,144×
336,215×
619,884×
31,952×
23,290×
42,196×
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0×
1×
123×
11,592×
225,672×
502,518×
403,212×
619,148×
1,107,198×
1,454,348×
2,117,376×
2,286,330×
3,228,266×
2,780,110×
4,413,232×
3,366,886×
5,859,918×
3,958,406×
7,339,640×
4,543,282×
8,946,302×
5,476,948×
10,654,890×
7,019,180×
12,168,226×
8,732,330×
13,233,370×
10,140,044×
13,541,230×
9,986,168×
13,023,136×
9,280,438×
12,278,614×
8,405,322×
11,464,932×
7,826,092×
9,954,898×
7,092,214×
8,215,508×
6,291,022×
6,493,060×
4,750,182×
4,654,866×
3,370,554×
2,778,420×
1,885,382×
1,275,506×
779,834×
391,214×
167,828×
64,892×
6,540×
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0×
1×
4,029×
84,328×
299,926×
447,066×
454,908×
786,940×
1,523,326×
1,844,014×
2,417,583×
2,630,074×
3,041,346×
2,014,032×
1,888,870×
1,917,131×
1,699,668×
2,039,642×
3,233,706×
2,905,947×
2,989,092×
3,053,576×
2,903,522×
3,245,886×
2,434,927×
2,299,786×
2,307,618×
2,313,309×
1,548,932×
1,594,942×
1,101,583×
1,308,548×
2,725,711×
2,790,962×
4,969,787×
5,322,350×
5,458,486×
5,589,634×
5,516,696×
4,933,032×
4,172,999×
4,220,170×
4,542,154×
4,537,002×
4,710,852×
4,195,218×
3,851,054×
3,973,628×
4,202,888×
4,480,502×
5,035,342×
4,357,096×
4,656,511×
3,715,564×
2,804,229×
2,512,026×
2,771,442×
2,908,378×
3,077,596×
3,351,628×
3,200,914×
3,485,230×
3,236,478×
3,990,084×
5,343,124×
4,086,726×
3,569,242×
3,504,076×
3,723,435×
2,784,274×
3,151,540×
3,596,987×
4,226,468×
4,092,587×
3,445,889×
3,208,492×
2,569,282×
2,832,418×
2,123,490×
2,851,101×
2,367,800×
1,957,202×
1,936,034×
2,061,794×
1,962,718×
2,463,560×
1,832,630×
2,097,894×
1,470,457×
1,401,283×
945,256×
879,815×
1,167,572×
1,399,608×
1,205,136×
1,911,413×
1,715,448×
1,481,096×
1,263,904×
1,102,642×
1,040,852×
989,442×
734,606×
965,868×
548,818×
2,677,464×
5,337,322×
5,263,906×
7,175,894×
9,568,887×
11,775,725×
12,467,185×
14,362,898×
13,434,088×
15,145,003×
15,126,871×
16,406,659×
16,235,340×
16,379,901×
16,736,317×
15,636,131×
14,479,417×
14,321,515×
14,355,294×
13,704,402×
11,931,794×
12,853,246×
14,608,820×
16,760,701×
16,394,959×
16,623,093×
17,191,627×
17,574,339×
19,003,868×
18,789,675×
19,392,942×
18,510,275×
17,114,248×
16,145,389×
14,664,764×
16,110,517×
17,081,578×
17,990,707×
18,419,676×
17,763,199×
15,487,551×
14,927,552×
14,930,196×
15,854,394×
14,486,518×
14,200,716×
12,878,915×
11,970,118×
11,831,124×
13,184,019×
13,469,348×
13,481,142×
12,425,301×
10,233,335×
9,748,568×
9,539,431×
9,910,880×
7,743,466×
7,599,272×
6,307,727×
6,294,515×
6,869,618×
7,674,346×
8,731,978×
10,031,198×
8,757,282×
7,931,603×
8,259,850×
8,375,710×
8,408,545×
10,299,146×
10,476,982×
9,830,289×
10,977,545×
10,390,213×
12,102,574×
11,849,381×
11,632,038×
13,007,908×
13,369,286×
15,547,317×
14,165,779×
15,205,066×
13,515,323×
14,614,718×
13,239,230×
13,176,040×
13,828,481×
12,333,600×
13,374,847×
12,187,054×
10,271,777×
10,356,216×
10,786,083×
10,664,790×
10,153,764×
12,917,051×
12,331,946×
10,316,431×
10,398,775×
9,679,196×
8,289,734×
8,968,229×
8,752,723×
9,008,378×
7,193,734×
7,768,893×
8,163,545×
9,058,439×
7,184,638×
7,332,606×
7,217,099×
7,229,193×
7,771,107×
5,634,655×
5,474,998×
5,803,828×
6,456,560×
5,962,148×
6,839,147×
8,594,640×
8,072,306×
8,709,033×
9,040,341×
8,687,751×
6,940,631×
8,514,579×
7,674,196×
9,397,662×
9,761,450×
9,416,886×
9,330,365×
10,409,296×
9,359,630×
8,396,804×
8,773,984×
8,419,200×
7,880,636×
9,108,808×
9,142,506×
9,389,009×
9,865,380×
10,721,528×
9,664,078×
8,901,991×
8,843,038×
9,907,198×
9,770,611×
8,246,448×
8,558,924×
8,074,484×
8,340,632×
8,316,645×
6,847,604×
6,992,744×
6,747,992×
6,494,484×
7,243,173×
7,223,157×
8,334,580×
7,979,505×
7,574,036×
7,765,119×
8,810,799×
8,707,737×
9,030,477×
9,575,181×
8,777,090×
8,231,876×
7,656,535×
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8,410,412×
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8,397,413×
7,706,525×
6,947,090×
7,267,605×
7,821,138×
9,301,695×
9,062,952×
8,820,969×
8,961,058×
9,126,589×
10,345,771×
11,313,465×
13,369,673×
14,987,898×
15,219,598×
15,526,151×
17,215,830×
18,101,540×
17,937,223×
17,900,755×
16,479,292×
17,532,158×
18,531,195×
17,836,087×
17,764,234×
19,233,328×
18,302,234×
19,387,044×
18,763,048×
18,625,876×
18,694,360×
17,879,001×
14,882,658×
14,612,845×
14,884,099×
14,774,663×
13,910,507×
14,231,730×
12,754,503×
13,528,859×
15,768,642×
13,342,302×
13,935,531×
12,659,514×
11,955,989×
10,592,912×
8,142,494×
9,727,507×
8,794,693×
8,756,461×
7,774,116×
8,383,469×
7,090,780×
6,187,419×
7,719,534×
7,416,334×
7,823,342×
7,766,013×
9,130,049×
9,311,690×
8,739,829×
9,412,155×
9,121,848×
9,117,884×
9,550,736×
7,884,332×
7,745,316×
9,224,614×
9,211,406×
9,954,740×
8,538,162×
8,618,948×
9,249,256×
8,883,834×
10,382,717×
10,585,262×
10,664,045×
10,166,130×
10,068,078×
9,979,241×
7,615,143×
9,157,426×
9,365,003×
8,456,283×
7,783,283×
8,492,110×
6,607,624×
6,546,106×
6,740,861×
5,713,996×
5,397,057×
5,649,030×
11,412,887×
24,635,745×
22,302,373×
27,077,268×
32,996,935×
37,013,176×
35,261,880×
35,723,452×
33,423,916×
34,441,787×
37,249,048×
36,475,744×
34,288,365×
33,882,633×
31,710,146×
31,391,710×
29,538,682×
32,436,435×
31,428,693×
32,334,027×
29,609,816×
29,220,811×
29,693,704×
27,961,104×
26,578,053×
29,538,524×
29,826,933×
29,852,222×
34,632,606×
32,101,196×
31,233,380×
29,309,192×
29,959,971×
31,672,702×
32,847,915×
32,969,367×
31,770,843×
32,241,113×
33,521,239×
34,214,656×
36,159,702×
33,489,102×
30,923,477×
29,629,427×
30,093,883×
29,490,914×
26,898,895×
28,035,349×
27,718,839×
27,961,725×
29,488,563×
26,115,856×
26,540,688×
27,071,611×
27,838,722×
26,019,115×
26,941,499×
25,349,091×
23,597,229×
22,410,422×
19,268,328×
20,050,500×
21,088,205×
21,845,773×
23,881,728×
21,760,135×
18,622,634×
17,328,145×
17,825,889×
15,092,124×
13,856,462×
13,912,629×
14,757,487×
15,838,909×
16,040,009×
18,008,426×
19,088,162×
20,116,449×
20,050,620×
17,663,979×
18,518,383×
18,389,653×
17,222,891×
14,632,176×
14,012,828×
11,094,501×
11,026,774×
12,118,373×
10,253,148×
9,482,426×
9,723,922×
8,271,864×
7,252,952×
6,008,106×
6,366,997×
6,995,483×
7,818,920×
7,441,417×
6,300,762×
7,060,086×
7,595,379×
7,557,235×
6,064,311×
6,343,788×
5,588,426×
4,423,293×
4,512,622×
4,442,975×
4,444,802×
3,830,468×
3,699,952×
3,127,101×
1,925,952×
2,171,884×
2,955,767×
2,154,560×
2,189,118×
2,544,303×
2,005,909×
1,843,690×
869,022×
1,138,196×
1,603,780×
2,521,857×
1,610,114×
1,641,286×
1,239,462×
1,183,986×
868,721×
1,209,729×
1,421,546×
1,582,846×
2,102,474×
2,102,502×
1,977,796×
1,633,461×
1,116,744×
796,378×
1,011,272×
976,722×
337,700×
513,082×
553,370×
526,226×
375,439×
166,844×