Base 125: 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		7.38 step
avg		26.60 step
avg		50.04 step
avg		28.03 step
avg		189.13 step
avg
Step Frequency
Full Cycle
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0×
1×
124×
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0×
2×
206×
106×
527×
338×
756×
1,452×
1,512×
2,976×
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0×
1×
124×
7,937×
3,965×
7,928×
7,918×
7,904×
7,886×
7,864×
7,838×
7,808×
7,774×
7,736×
7,694×
7,648×
7,598×
7,544×
7,486×
7,424×
7,358×
7,288×
7,214×
7,136×
7,054×
6,968×
6,878×
6,784×
6,686×
6,584×
6,478×
6,368×
6,254×
6,136×
6,014×
5,888×
5,758×
5,624×
5,486×
5,344×
5,198×
5,048×
4,894×
4,736×
4,574×
4,408×
4,238×
4,064×
3,886×
3,704×
3,518×
3,328×
3,134×
2,936×
2,734×
2,528×
2,318×
2,104×
1,886×
1,664×
1,438×
1,208×
974×
736×
494×
248×
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0×
1×
2,674×
3,875×
0×
0×
6,810×
20,275×
0×
0×
0×
93,600×
241,500×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
32,730×
101,687×
7,721×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
2,485,236×
7,421,878×
246,045×
3,968×
0s:
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0×
1×
124×
0×
0×
303,240×
311,278×
433,880×
946,196×
1,341,840×
2,067,130×
2,302,783×
3,339,008×
2,922,511×
5,029,141×
4,185,078×
6,573,630×
4,809,771×
8,134,799×
5,419,784×
9,686,260×
6,302,225×
11,322,417×
8,333,905×
13,140,023×
10,523,124×
14,082,221×
10,732,831×
13,114,811×
10,031,810×
12,455,082×
9,170,922×
12,006,049×
8,468,801×
10,686,946×
7,955,015×
8,962,001×
7,175,741×
7,395,629×
6,071,245×
5,854,524×
5,004,353×
4,376,081×
3,751,546×
3,060,466×
2,522,341×
1,803,210×
1,226,953×
808,297×
607,883×
361,270×
120,224×
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0×
1×
93,548×
176,928×
1,483,344×
2,159,326×
7,133,556×
5,490,450×
9,711,086×
30,640,965×
16,605,807×
7,871,264×
9,129,748×
12,114,770×
16,812,124×
19,876,422×
21,190,155×
19,784,124×
20,797,725×
22,617,359×
25,679,758×
22,823,117×
23,311,842×
22,601,379×
21,777,355×
25,489,270×
27,616,391×
25,565,818×
27,468,990×
29,489,202×
29,782,229×
31,516,346×
28,869,578×
29,675,175×
30,735,438×
34,448,448×
30,872,172×
31,569,019×
31,300,051×
32,394,693×
33,826,724×
30,387,087×
29,659,394×
27,223,470×
27,403,321×
32,076,423×
32,027,965×
28,409,155×
24,989,750×
23,012,435×
21,277,215×
23,654,416×
24,339,477×
22,317,685×
24,898,794×
26,311,690×
26,648,767×
24,908,900×
25,208,178×
24,128,462×
29,151,300×
25,841,910×
25,153,066×
25,648,993×
23,168,429×
24,595,651×
23,955,170×
25,387,636×
24,803,975×
23,855,393×
24,541,831×
25,184,999×
22,960,724×
22,008,653×
24,175,231×
26,441,581×
28,026,106×
24,863,549×
25,330,974×
22,559,854×
21,326,984×
23,401,445×
20,359,417×
22,211,676×
21,099,106×
21,546,930×
18,031,712×
18,201,227×
21,941,240×
21,814,805×
24,256,482×
24,305,015×
22,223,721×
27,119,793×
25,572,474×
27,675,643×
23,585,893×
21,114,554×
18,602,529×
23,368,261×
18,959,285×
19,899,929×
20,105,806×
20,930,187×
22,582,047×
20,677,136×
13,744,333×
15,636,000×
16,738,210×
17,231,224×
15,238,581×
16,987,557×
14,131,753×
11,370,673×
13,866,789×
15,248,203×
14,282,450×
15,035,258×
17,613,193×
15,612,789×
15,914,945×
16,694,622×
16,105,517×
13,142,533×
14,603,810×
18,113,060×
15,553,941×
14,406,426×
13,053,738×
12,065,869×
10,517,821×
11,403,291×
10,481,792×
10,037,612×
8,754,460×
10,769,050×
13,177,343×
12,991,031×
14,294,052×
14,489,927×
10,669,130×
13,314,609×
12,240,751×
10,992,807×
12,371,675×
11,958,550×
12,887,214×
12,474,012×
16,947,289×
17,164,497×
16,198,437×
15,112,570×
13,114,057×
10,438,355×
9,150,407×
8,317,734×
7,804,634×
9,783,452×
12,793,279×
10,496,972×
9,629,742×
10,379,846×
10,957,697×
12,297,877×
11,933,738×
10,056,960×
9,276,889×
11,617,664×
13,671,706×
13,428,931×
12,718,689×
13,901,195×
13,129,338×
13,644,026×
14,000,272×
16,350,579×
12,276,704×
8,718,866×
10,569,117×
12,334,639×
13,515,437×
12,912,001×
10,556,523×
11,174,154×
11,237,467×
11,844,683×
11,152,790×
12,606,185×
11,808,918×
11,680,144×
13,417,157×
14,703,534×
16,314,121×
14,482,775×
14,823,895×
15,949,644×
11,675,222×
10,355,542×
9,621,910×
10,976,494×
10,644,682×
9,979,568×
12,879,732×
12,199,608×
10,723,086×
12,732,013×
11,732,157×
12,770,386×
14,327,847×
10,816,115×
8,883,925×
7,620,518×
7,684,340×
8,454,783×
8,572,593×
9,261,957×
9,567,829×
9,804,924×
8,229,724×
5,966,540×
5,621,383×
5,555,448×
4,908,853×
4,199,220×
3,808,665×
2,874,274×
3,329,011×
3,169,002×
4,652,042×
4,256,269×
4,611,275×
4,847,550×
3,304,104×
3,432,612×
4,491,688×
4,720,995×
4,224,573×
4,336,658×
5,189,932×
5,166,656×
4,657,039×
4,250,692×
3,983,537×
4,304,337×
4,518,478×
6,094,986×
5,844,041×
3,309,142×
3,493,057×
5,699,919×
5,725,639×
4,291,553×
3,628,681×
3,806,508×
3,482,335×
4,150,936×
3,821,883×
4,021,436×
3,461,977×
3,690,161×
3,851,774×
3,443,260×
3,329,814×
3,292,776×
3,325,466×
3,133,119×
4,210,570×
3,010,868×
3,474,254×
1,947,608×
2,982,356×
3,114,496×
3,616,616×
4,259,964×
4,648,636×
4,193,082×
4,269,191×
5,684,938×
6,400,744×
8,352,116×
8,368,100×
8,523,464×
6,913,310×
7,754,405×
9,657,701×
8,054,829×
9,107,325×
10,280,608×
10,323,834×
9,941,914×
10,490,066×
11,123,830×
11,037,734×
14,354,975×
15,222,843×
12,945,933×
15,416,337×
15,325,864×
13,591,994×
18,682,191×
21,440,378×
21,371,033×
21,501,532×
23,592,692×
22,283,234×
24,093,010×
23,587,598×
19,213,453×
15,604,818×
16,189,062×
18,897,374×
16,411,969×
15,840,961×
12,420,978×
13,009,018×
14,860,317×
13,742,318×
10,775,579×
11,606,267×
8,032,404×
7,028,864×
6,239,476×
5,116,298×
5,488,666×
5,859,553×
6,676,043×
7,463,259×
7,797,167×
8,838,370×
7,468,221×
7,360,997×
7,687,248×
9,905,257×
9,188,412×
9,219,147×
10,684,720×
10,250,497×
5,399,115×
6,664,136×
7,900,150×
8,636,964×
7,625,545×
6,999,424×
7,641,991×
9,719,211×
11,890,226×
13,809,693×
13,553,149×
10,392,055×
10,025,357×
9,247,157×
10,508,462×
9,299,775×
10,622,169×
14,856,780×
16,680,991×
14,545,850×
13,201,921×
14,865,133×
11,395,838×
13,442,474×
13,841,884×
9,352,955×
10,765,695×
7,593,254×
11,024,400×
13,099,412×
8,638,421×
8,289,772×
9,376,176×
10,525,726×
11,557,608×
12,007,379×
12,714,913×
10,724,408×
7,363,252×
9,052,885×
11,138,671×
11,442,091×
11,378,165×
11,204,199×
11,773,137×
12,711,049×
10,304,464×
10,431,268×
12,725,016×
12,653,516×
10,422,480×
9,669,132×
7,713,069×
7,158,415×
7,688,736×
8,230,212×
6,694,814×
6,152,561×
6,895,118×
7,721,181×
6,981,076×
6,015,857×
5,692,720×
6,232,289×
4,866,836×
4,880,260×
3,241,515×
2,870,113×
3,588,788×
4,318,415×
4,851,297×
4,504,653×
3,942,904×
3,426,815×
4,238,994×
6,218,478×
6,738,477×
5,029,312×
5,223,412×
4,534,516×
3,171,251×
3,178,129×
3,409,787×
3,483,539×
2,810,084×
3,121,254×
3,032,480×
2,960,608×
3,355,801×
4,200,159×
3,890,825×
2,530,485×
4,011,528×
3,780,113×
4,064,919×
5,867,177×
4,713,517×
4,528,493×
3,810,392×
5,147,557×
4,635,943×
4,185,590×
5,020,565×
5,382,655×
6,440,966×
6,958,740×
7,635,676×
7,648,183×
7,024,576×
7,195,673×
7,653,457×
6,922,366×
6,994,633×
7,270,648×
8,137,087×
6,378,344×
5,721,844×
6,014,195×
4,698,324×
5,151,612×
5,522,359×
6,789,713×
6,016,314×
6,754,146×
6,660,897×
6,816,746×
10,427,229×
9,361,155×
8,399,035×
8,372,165×
7,189,978×
6,922,171×
9,781,039×
8,500,689×
6,909,303×
7,480,726×
6,734,058×
4,639,060×
5,551,266×
6,387,483×
5,132,512×
4,513,506×
4,370,791×
3,606,295×
3,080,271×
3,726,786×
5,166,311×
5,435,756×
6,167,912×
6,603,386×
7,483,184×
6,183,815×
6,924,988×
5,686,561×
4,652,044×
4,245,921×
1,916,754×
2,021,914×
1,882,655×
1,260,806×
1,121,928×
789,955×
871,057×
1,572,775×
1,708,426×
1,947,535×
2,166,083×
3,127,421×
2,682,513×
3,133,172×
3,254,002×
2,381,959×
2,567,817×
1,826,327×
1,899,777×
2,233,143×
1,043,774×
981,808×
578,191×
309,994×
416,420×
372,915×
380,755×
360,463×
561,793×
362,500×
192,787×
33,313×
18,552×
163,916×
520,866×
639,034×
624,534×
74,253×
190,338×
494,046×
735,722×
646,100×
694,319×
743,889×
278,192×
518,793×
482,822×
198,857×
231,009×
14,757×
8,424×
15,300×
76,094×
3,051×