Base 126: 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		8.39 step
avg		26.29 step
avg		8.61 step
avg		27.63 step
avg		232.82 step
avg
Step Frequency
Full Cycle
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0×
1×
125×
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1×
125×
0×
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0×
32×
3,937×
3,906×
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0×
1×
4,157×
4,030×
8,058×
8,050×
8,038×
8,022×
8,002×
7,978×
7,950×
7,918×
7,882×
7,842×
7,798×
7,750×
7,698×
7,642×
7,582×
7,518×
7,450×
7,378×
7,302×
7,222×
7,138×
7,050×
6,958×
6,862×
6,762×
6,658×
6,550×
6,438×
6,322×
6,202×
6,078×
5,950×
5,818×
5,682×
5,542×
5,398×
5,250×
5,098×
4,942×
4,782×
4,618×
4,450×
4,278×
4,102×
3,922×
3,738×
3,550×
3,358×
3,162×
2,962×
2,758×
2,550×
2,338×
2,122×
1,902×
1,678×
1,450×
1,218×
982×
742×
498×
250×
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0×
1×
125×
0×
58,128×
135,006×
540,540×
629,783×
1,780,488×
7,076,160×
402,319×
356,359×
18,423×
12,044×
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0×
1×
77,783×
110,252×
179,498×
375,226×
630,546×
1,071,820×
1,380,694×
1,972,722×
1,890,094×
3,392,244×
3,294,038×
4,874,566×
3,923,424×
6,412,950×
4,554,176×
7,979,292×
5,174,738×
9,602,918×
6,283,136×
11,339,094×
8,183,154×
12,907,362×
9,476,000×
13,380,924×
9,996,090×
13,499,980×
10,306,282×
13,556,226×
9,672,664×
12,776,134×
9,015,994×
11,238,530×
8,479,292×
10,181,614×
7,513,516×
8,660,398×
6,526,528×
6,871,728×
5,604,848×
5,288,912×
4,316,668×
3,901,674×
3,065,948×
2,461,874×
1,835,996×
1,365,306×
904,278×
478,714×
196,842×
54,048×
7,040×
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0×
1×
4,157×
0×
0×
0×
0×
0×
11,100,960×
32,103,304×
3,927,904×
838,048×
1,481,981×
2,237,960×
3,163,501×
2,795,673×
3,306,214×
2,626,214×
2,407,821×
3,472,347×
3,243,555×
3,780,066×
4,874,736×
5,438,505×
3,797,423×
2,679,425×
2,754,761×
3,137,390×
4,422,015×
5,140,471×
3,701,882×
3,655,650×
3,759,575×
4,359,836×
5,013,699×
5,944,030×
6,858,536×
4,785,679×
5,343,184×
7,417,110×
8,373,945×
9,074,332×
10,769,390×
10,707,633×
10,750,001×
11,305,427×
12,743,266×
15,441,352×
16,435,674×
17,791,236×
16,449,643×
17,658,026×
18,162,632×
17,115,226×
16,731,058×
16,132,729×
15,392,498×
16,387,436×
19,302,398×
20,890,853×
17,898,097×
18,060,056×
20,322,292×
21,406,166×
23,124,738×
20,164,298×
18,747,868×
19,097,971×
19,502,586×
16,386,292×
16,380,325×
13,679,629×
16,233,237×
19,964,237×
18,413,208×
17,738,068×
19,152,116×
18,204,270×
18,584,508×
18,761,861×
18,461,815×
17,733,263×
17,597,843×
17,131,698×
17,023,131×
16,613,973×
18,656,315×
19,934,016×
18,399,921×
19,261,538×
20,481,648×
19,898,171×
18,044,255×
18,487,991×
21,569,613×
20,409,713×
21,945,448×
19,461,033×
18,064,238×
18,641,895×
18,179,696×
17,703,641×
18,897,799×
16,082,764×
17,541,267×
19,386,490×
22,180,039×
21,634,166×
18,003,325×
15,566,665×
13,770,463×
13,437,237×
14,130,494×
12,873,151×
11,490,458×
9,504,429×
9,420,707×
11,338,102×
10,363,687×
9,474,025×
9,111,586×
9,122,796×
7,390,062×
6,919,200×
5,799,632×
7,344,038×
8,292,687×
8,604,932×
6,974,373×
6,369,795×
7,573,044×
8,142,114×
7,762,865×
6,523,177×
9,710,489×
15,435,290×
14,497,718×
15,672,305×
16,386,423×
16,851,762×
15,581,078×
18,018,018×
19,637,035×
22,446,260×
23,551,665×
23,122,977×
22,944,909×
22,833,350×
20,265,593×
21,659,085×
20,416,526×
21,695,864×
24,877,201×
22,643,439×
24,482,680×
21,108,814×
21,949,813×
20,969,144×
19,412,949×
18,699,678×
19,940,342×
20,500,409×
17,894,110×
18,894,676×
18,061,037×
20,229,002×
20,698,664×
20,177,419×
19,779,505×
20,263,140×
17,273,643×
18,010,972×
15,880,165×
17,328,032×
17,912,675×
17,152,014×
18,115,632×
17,574,377×
15,831,741×
18,712,282×
18,439,088×
19,671,486×
20,892,385×
20,523,299×
19,525,201×
18,336,198×
20,566,679×
23,516,239×
21,288,235×
18,932,667×
18,905,873×
17,338,343×
17,391,235×
17,049,239×
17,580,851×
19,812,478×
19,488,882×
19,435,310×
20,045,644×
17,909,498×
16,323,564×
16,544,224×
13,338,183×
14,493,665×
13,602,246×
13,809,980×
13,641,810×
13,056,747×
13,758,381×
14,201,557×
13,745,364×
13,107,960×
14,855,612×
15,153,299×
14,293,306×
13,018,510×
12,539,538×
12,307,737×
13,411,017×
13,150,075×
13,557,575×
14,176,421×
12,884,407×
14,448,511×
14,600,980×
13,474,186×
11,876,867×
12,565,137×
14,086,701×
15,172,053×
16,600,666×
15,357,810×
14,011,904×
12,934,536×
14,782,036×
13,905,569×
15,271,732×
12,314,805×
10,416,487×
11,670,166×
10,574,363×
10,148,838×
11,339,187×
10,524,835×
12,429,156×
13,469,857×
13,290,754×
9,843,439×
9,157,332×
8,583,502×
9,969,847×
11,519,198×
10,334,091×
9,157,222×
9,341,031×
10,360,389×
12,018,015×
11,078,868×
11,707,028×
13,921,436×
14,901,244×
13,664,483×
15,230,558×
12,396,090×
11,904,152×
12,830,410×
16,329,446×
13,843,454×
10,783,226×
11,520,388×
10,251,737×
10,998,334×
9,611,561×
10,063,839×
9,576,288×
11,814,260×
14,116,351×
13,792,121×
14,567,527×
13,870,348×
15,057,879×
13,615,111×
13,410,314×
12,809,959×
12,528,591×
12,544,696×
12,168,539×
12,491,303×
12,021,679×
11,326,040×
14,541,464×
17,601,938×
17,039,854×
17,134,076×
16,961,594×
15,706,408×
18,573,875×
17,143,372×
17,363,352×
14,952,388×
14,784,076×
12,641,240×
13,289,169×
14,576,795×
13,503,846×
13,450,700×
15,226,077×
13,192,275×
12,024,934×
12,577,323×
13,280,943×
13,623,060×
14,722,891×
14,071,125×
13,904,459×
15,078,461×
16,036,719×
15,882,313×
15,721,951×
15,912,929×
14,916,269×
16,412,689×
15,474,470×
16,184,100×
17,313,479×
16,944,640×
14,999,897×
13,718,111×
12,512,524×
12,651,710×
12,757,862×
12,839,432×
12,575,719×
12,462,425×
12,638,586×
13,105,808×
13,335,640×
12,302,585×
12,441,428×
12,485,891×
10,523,803×
9,436,184×
11,226,624×
10,679,261×
9,391,067×
10,522,713×
8,993,911×
11,361,044×
10,087,173×
8,153,232×
8,562,704×
9,271,803×
10,746,603×
10,708,542×
11,995,698×
8,925,575×
7,816,626×
8,154,664×
8,647,895×
7,204,790×
7,385,825×
8,569,521×
7,151,294×
8,300,689×
8,083,198×
7,328,214×
8,014,773×
8,908,520×
8,169,139×
7,534,033×
7,485,585×
8,035,525×
7,850,293×
8,900,026×
10,764,252×
10,482,946×
11,748,591×
12,229,203×
11,549,255×
12,904,607×
13,657,014×
15,471,146×
16,265,268×
15,362,983×
13,614,356×
11,813,325×
14,606,737×
13,924,871×
14,516,254×
15,431,597×
17,583,192×
18,723,278×
16,334,173×
17,133,750×
16,207,760×
17,546,195×
18,986,438×
19,404,427×
17,391,155×
15,825,056×
16,027,508×
18,062,380×
18,249,646×
17,280,010×
16,143,845×
15,270,526×
12,925,466×
12,568,828×
13,838,341×
13,664,052×
11,792,452×
10,633,514×
11,101,598×
10,856,169×
11,305,342×
11,805,340×
9,233,190×
10,754,141×
10,696,424×
10,423,739×
10,171,436×
10,727,403×
12,020,899×
14,612,744×
13,336,109×
9,507,636×
8,345,068×
7,450,991×
6,944,629×
6,689,865×
5,710,752×
4,772,319×
6,024,497×
6,325,686×
4,884,520×
4,412,147×
4,277,503×
4,056,237×
5,237,358×
6,328,682×
4,648,342×
4,728,677×
5,007,021×
5,534,983×
5,029,131×
6,080,119×
3,751,354×
2,877,461×
2,680,945×
3,210,388×
2,881,852×
4,359,840×
4,426,852×
5,183,937×
7,139,086×
6,380,078×
7,249,962×
7,386,356×
8,046,574×
8,485,116×
7,850,633×
6,544,673×
7,528,948×
6,159,343×
5,873,199×
5,439,518×
3,566,933×
4,274,046×
5,000,185×
4,988,772×
4,153,888×
4,898,783×
4,438,814×
5,220,668×
3,970,253×
3,917,541×
3,664,790×
1,838,046×
2,752,231×
3,113,934×
4,220,490×
5,086,746×
4,467,707×
4,261,596×
3,925,004×
5,697,631×
6,113,992×
6,299,966×
5,935,846×
5,423,650×
4,865,803×
5,346,221×
4,891,195×
3,633,526×
4,232,645×
5,601,769×
6,394,393×
5,634,351×
7,160,164×
6,344,557×
6,458,484×
7,132,598×
7,355,424×
4,797,050×
4,372,445×
3,960,023×
4,118,370×
3,400,387×
2,790,087×
2,225,994×
2,185,776×
1,506,376×
1,752,464×
2,695,686×
1,914,503×
1,515,577×
1,876,260×
1,226,788×
1,679,696×
2,398,203×
2,471,532×
1,276,234×
807,314×
395,552×
101,202×