Base 133: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

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

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		34.51 step
avg		28.10 step
avg		19.37 step
avg		29.82 step
avg		312.74 step
avg
Step Frequency
Full Cycle
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132×
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17×
2,194×
2,145×
4,356×
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0×
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132×
8,977×
4,485×
8,968×
8,958×
8,944×
8,926×
8,904×
8,878×
8,848×
8,814×
8,776×
8,734×
8,688×
8,638×
8,584×
8,526×
8,464×
8,398×
8,328×
8,254×
8,176×
8,094×
8,008×
7,918×
7,824×
7,726×
7,624×
7,518×
7,408×
7,294×
7,176×
7,054×
6,928×
6,798×
6,664×
6,526×
6,384×
6,238×
6,088×
5,934×
5,776×
5,614×
5,448×
5,278×
5,104×
4,926×
4,744×
4,558×
4,368×
4,174×
3,976×
3,774×
3,568×
3,358×
3,144×
2,926×
2,704×
2,478×
2,248×
2,014×
1,776×
1,534×
1,288×
1,038×
784×
526×
264×
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0×
1×
132×
0×
7,372×
13,395×
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0×
161,334×
411,024×
10,049×
0×
0×
0×
0×
0×
0×
3,184,644×
9,546,454×
294,937×
4,488×
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0×
1×
132×
0×
272,841×
613,734×
487,893×
754,472×
1,346,607×
1,770,887×
2,572,149×
2,784,927×
3,918,302×
3,388,513×
5,356,315×
4,108,528×
7,116,846×
4,838,363×
8,926,181×
5,565,766×
10,826,749×
6,410,742×
12,800,921×
7,789,653×
14,965,237×
9,974,051×
16,758,769×
12,125,912×
17,676,509×
13,492,708×
17,990,557×
13,025,504×
16,806,202×
12,064,764×
16,126,743×
11,110,397×
15,299,237×
10,405,180×
13,350,158×
9,431,402×
11,184,655×
8,594,497×
9,098,767×
6,949,255×
7,019,720×
5,019,693×
4,508,479×
3,209,030×
2,358,517×
1,579,935×
967,158×
503,585×
229,095×
81,320×
9,384×
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0×
1×
132×
0×
0×
63,344×
151,550×
321,315×
318,252×
483,079×
797,148×
1,295,153×
1,038,927×
1,275,080×
612,638×
603,575×
1,065,814×
2,128,842×
1,541,265×
1,326,225×
2,262,277×
2,999,962×
2,322,140×
720,332×
1,125,501×
2,709,958×
3,578,866×
5,846,805×
5,736,390×
6,361,909×
7,796,025×
7,147,029×
8,209,752×
8,619,770×
8,320,717×
8,456,586×
8,077,261×
8,835,365×
13,134,222×
9,976,639×
8,751,304×
8,381,344×
7,903,200×
9,090,284×
9,315,028×
7,845,983×
8,487,289×
8,079,684×
8,534,291×
8,055,140×
7,642,148×
6,044,415×
6,291,259×
8,009,265×
6,002,947×
6,779,222×
9,010,523×
8,667,404×
9,064,233×
8,318,201×
6,898,668×
7,083,392×
6,195,914×
5,509,502×
6,608,022×
7,320,162×
7,415,863×
8,243,223×
6,236,857×
5,931,666×
5,315,608×
6,217,791×
6,719,305×
5,623,471×
7,072,531×
7,762,203×
5,771,189×
9,194,207×
9,721,564×
12,094,884×
13,730,346×
14,752,172×
15,267,710×
12,881,326×
16,091,008×
14,244,829×
13,067,735×
13,219,096×
12,501,068×
12,523,250×
10,123,970×
11,281,032×
11,207,938×
12,616,074×
12,785,309×
14,642,131×
14,166,514×
13,147,635×
11,344,611×
9,698,639×
10,665,359×
11,340,286×
9,807,116×
8,699,109×
9,069,864×
8,381,528×
7,873,554×
6,262,882×
8,814,376×
9,583,456×
7,701,966×
6,937,486×
6,125,136×
7,699,181×
7,163,896×
4,828,049×
5,075,411×
5,130,816×
5,692,104×
4,802,821×
5,213,714×
5,135,801×
5,495,762×
7,418,291×
8,320,405×
9,872,017×
6,979,102×
7,046,041×
6,221,504×
6,975,037×
6,866,875×
4,323,498×
3,746,621×
4,215,599×
5,092,905×
4,718,432×
4,396,952×
3,719,165×
5,081,256×
3,746,380×
4,853,384×
3,870,792×
3,960,932×
3,654,517×
4,463,948×
4,600,706×
4,120,079×
3,876,631×
3,642,113×
3,905,147×
4,023,226×
5,151,803×
6,059,233×
8,349,050×
7,830,085×
5,560,851×
4,423,367×
6,124,370×
6,210,867×
5,825,292×
4,764,166×
5,991,088×
6,424,293×
6,194,643×
6,016,755×
7,236,227×
6,900,198×
7,845,205×
7,339,331×
7,990,096×
6,812,885×
5,806,287×
6,556,337×
5,136,808×
4,196,334×
3,691,145×
3,359,459×
3,789,491×
4,061,397×
5,973,245×
5,548,458×
5,151,277×
4,662,064×
5,315,562×
3,687,961×
2,760,574×
3,718,962×
2,713,450×
2,980,155×
2,597,040×
3,436,086×
1,414,638×
1,127,772×
1,014,612×
995,532×
1,259,808×
1,267,332×
1,331,779×
5,950,639×
16,047,471×
36,369,770×
27,211,022×
24,155,329×
22,173,432×
21,028,917×
22,085,562×
25,115,886×
22,843,721×
20,883,554×
20,898,838×
20,353,899×
17,311,306×
20,025,387×
21,702,372×
19,707,975×
20,275,779×
24,979,013×
25,257,727×
23,162,541×
20,429,041×
16,651,577×
16,134,887×
14,730,734×
17,013,752×
14,104,444×
14,471,047×
15,150,428×
15,202,814×
14,881,462×
14,682,211×
13,466,404×
15,245,570×
16,371,691×
17,075,154×
16,826,929×
21,279,180×
21,664,997×
21,425,007×
24,833,851×
24,112,831×
21,776,824×
19,193,898×
19,058,731×
20,497,629×
21,047,246×
23,354,676×
22,069,881×
21,446,696×
25,038,918×
29,677,547×
30,686,089×
24,575,240×
24,514,447×
28,393,306×
26,160,302×
30,303,812×
27,551,643×
29,084,467×
30,591,344×
29,180,740×
32,335,303×
35,968,712×
34,357,419×
36,048,875×
31,632,155×
32,574,600×
31,360,345×
31,224,127×
33,033,929×
34,889,181×
35,620,041×
35,845,787×
29,702,414×
28,041,233×
26,035,720×
27,946,369×
26,140,725×
26,376,000×
25,499,130×
25,351,620×
27,762,929×
29,126,566×
28,722,071×
28,817,118×
25,124,673×
22,542,886×
21,100,135×
21,610,617×
22,460,474×
22,907,887×
19,839,522×
17,254,721×
22,750,657×
24,502,052×
24,059,509×
26,042,878×
29,148,777×
26,807,372×
26,248,230×
23,038,546×
21,929,239×
24,141,435×
23,095,742×
24,924,370×
26,615,539×
26,873,847×
27,054,701×
27,803,847×
27,148,294×
24,024,322×
21,706,717×
25,077,281×
27,039,794×
28,549,733×
29,627,645×
30,382,426×
26,751,273×
26,410,901×
26,298,038×
27,840,344×
27,996,516×
27,388,798×
26,933,528×
28,768,783×
27,919,739×
29,045,197×
30,964,942×
32,049,360×
31,251,476×
30,148,073×
32,676,262×
28,482,825×
25,616,846×
26,575,554×
27,329,363×
27,071,969×
26,006,831×
24,359,562×
26,019,244×
29,156,759×
25,536,771×
27,414,823×
24,833,837×
23,476,115×
23,801,939×
23,799,787×
24,081,548×
19,937,028×
19,888,419×
20,468,337×
24,173,372×
24,565,898×
25,806,280×
26,372,657×
28,922,601×
29,917,545×
27,730,645×
26,845,158×
23,693,038×
22,947,927×
24,507,548×
23,611,072×
21,656,952×
21,490,603×
21,822,128×
24,185,734×
20,758,365×
23,349,249×
26,066,879×
25,056,763×
26,807,229×
23,702,213×
26,667,241×
25,445,299×
26,763,744×
30,722,565×
29,667,100×
27,215,604×
27,477,761×
24,422,907×
26,623,591×
26,174,707×
25,880,709×
23,810,444×
29,229,726×
23,449,452×
27,981,658×
30,674,725×
34,101,408×
30,963,555×
30,154,007×
26,872,575×
27,043,409×
27,600,184×
27,358,546×
27,647,004×
31,354,596×
31,249,799×
30,705,489×
30,748,626×
29,335,018×
27,764,238×
29,511,927×
25,853,590×
25,887,148×
33,565,136×
34,232,514×
28,706,932×
29,935,218×
28,414,013×
26,156,179×
25,345,750×
28,992,213×
31,752,171×
32,115,290×
29,107,267×
27,766,081×
26,632,355×
23,873,624×
24,159,593×
24,615,454×
23,685,649×
24,776,516×
23,484,868×
22,972,202×
23,220,325×
22,908,441×
21,066,059×
21,140,270×
23,609,163×
25,178,422×
27,423,546×
26,726,313×
25,178,614×
25,039,765×
25,668,234×
25,037,765×
23,529,917×
23,441,474×
22,696,195×
24,447,238×
24,026,994×
25,944,035×
27,504,702×
20,932,303×
22,387,379×
24,896,500×
27,220,494×
25,148,227×
22,141,114×
23,069,741×
24,519,596×
20,583,236×
21,074,584×
24,244,249×
20,965,662×
15,744,988×
17,828,163×
16,624,602×
14,392,780×
13,628,187×
12,223,164×
12,183,424×
11,432,923×
10,357,839×
10,659,912×
12,243,846×
14,211,372×
16,074,353×
13,479,742×
12,922,551×
14,319,874×
11,398,203×
12,459,093×
13,639,889×
14,660,668×
12,637,583×
15,727,871×
16,706,997×
12,977,562×
9,898,175×
9,758,927×
9,611,652×
10,235,839×
9,521,084×
12,686,285×
14,121,629×
12,342,658×
13,341,778×
12,929,906×
9,472,020×
9,904,867×
12,049,433×
11,732,417×
11,290,325×
9,515,056×
7,736,545×
7,129,563×
7,228,380×
8,885,985×
8,881,504×
9,467,576×
8,516,966×
8,079,138×
9,216,914×
9,966,239×
9,221,204×
10,030,448×
8,594,983×
7,887,216×
9,330,968×
8,727,418×
5,661,869×
6,534,880×
7,514,462×
6,537,406×
6,130,379×
7,004,400×
5,450,856×
4,249,063×
5,258,093×
4,922,173×
4,910,889×
3,748,890×
3,201,910×
4,353,241×
3,800,207×
3,523,689×
4,287,340×
2,587,532×
3,130,887×
3,921,697×
3,187,525×
3,160,751×
2,205,665×
2,279,359×
2,732,839×
3,264,293×
3,796,348×
3,507,440×
3,586,333×
1,792,995×
2,096,306×
2,331,649×
1,981,964×
1,808,365×
2,445,253×
1,519,069×
1,350,192×
790,933×
619,381×
1,114,364×
1,472,084×
1,026,680×
1,341,870×
697,717×
1,051,341×
275,932×
564,446×
486,186×
185,217×
270,279×
701,246×
906,008×
902,898×
494,821×
834,868×
1,404,998×
2,257,619×
2,498,872×
4,203,481×
4,648,976×
2,871,065×
2,123,481×
2,071,238×
1,905,680×
2,291,920×
2,367,680×
2,023,172×
2,376,680×
2,385,224×
1,702,647×
1,593,487×
256,057×
108,862×
407,833×
108,152×
141,445×
82,511×
18,998×