Base 125: Iteration Frequencies: Cycle Start

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
Cycle Start		0.99 step
avg		2.22 step
avg		24.60 step
avg		1.78 step
avg		24.03 step
avg		178.38 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
124×
0s:
1s:
2s:
3s:
17×
2,061×
1,953×
3,844×
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1×
8,061×
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×
0s:
1s:
2s:
3s:
4s:
1×
2,621,050×
7,789,215×
253,766×
3,968×
0s:
1s:
2s:
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47s:
1×
303,364×
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×
0s:
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532s:
533s:
534s:
1×
5,038,065×
15,755,942×
46,723,575×
25,689,342×
15,693,572×
18,029,144×
21,023,466×
24,990,781×
25,861,029×
25,078,523×
25,124,631×
24,799,988×
31,698,663×
33,809,784×
26,818,617×
27,953,412×
28,603,672×
29,588,077×
34,580,921×
37,630,729×
34,852,855×
32,524,874×
31,003,149×
30,320,885×
30,711,055×
24,734,161×
27,938,227×
29,127,822×
32,158,306×
27,927,425×
29,315,112×
25,150,865×
28,698,719×
29,927,855×
28,196,997×
28,206,931×
24,063,545×
22,942,928×
27,531,176×
26,103,613×
24,148,705×
23,421,251×
24,214,942×
23,818,657×
24,428,420×
24,766,469×
28,600,169×
32,071,911×
31,011,074×
25,264,938×
26,743,266×
24,116,018×
27,990,268×
32,577,109×
29,694,159×
22,215,364×
25,035,755×
23,502,026×
24,855,242×
23,883,636×
26,204,682×
27,292,745×
29,053,117×
30,566,102×
33,294,600×
29,509,298×
26,370,179×
24,277,201×
22,561,380×
20,141,540×
20,426,787×
22,333,834×
21,446,039×
22,494,743×
20,410,677×
17,859,084×
19,916,548×
18,956,988×
20,244,390×
18,450,256×
22,729,757×
25,186,131×
24,769,198×
21,511,157×
20,306,925×
16,957,892×
19,023,512×
14,734,503×
15,371,488×
15,891,603×
17,209,477×
17,680,623×
19,921,414×
13,883,399×
15,044,055×
15,630,831×
16,735,777×
17,824,785×
16,821,571×
14,072,342×
15,071,518×
17,062,322×
17,944,929×
15,282,878×
17,916,238×
18,301,347×
13,436,434×
13,560,969×
13,009,068×
11,886,162×
12,723,434×
15,388,535×
17,623,385×
18,060,213×
20,391,739×
20,953,933×
15,555,208×
13,489,650×
14,865,452×
11,775,432×
10,881,730×
8,394,563×
10,340,542×
10,590,866×
10,885,575×
11,372,780×
10,414,951×
8,771,088×
11,570,432×
13,823,621×
12,946,326×
14,537,496×
14,160,886×
12,076,187×
13,617,795×
16,081,293×
15,375,669×
15,414,531×
13,918,060×
13,322,326×
11,240,329×
10,638,984×
11,299,936×
9,701,056×
10,149,086×
9,754,212×
7,372,431×
5,820,624×
5,257,793×
7,116,106×
10,172,282×
13,688,819×
10,999,738×
10,955,072×
13,463,853×
14,512,256×
13,793,323×
13,490,195×
13,906,973×
13,456,385×
13,633,931×
14,562,067×
16,749,422×
11,431,694×
10,316,041×
9,504,143×
12,847,565×
13,152,964×
13,599,258×
12,126,573×
9,653,628×
11,799,128×
11,629,077×
12,776,932×
13,228,432×
12,100,867×
12,829,563×
13,465,848×
14,348,081×
15,710,212×
15,391,330×
13,907,649×
13,108,339×
11,673,274×
11,582,596×
11,169,778×
12,033,023×
13,238,658×
13,155,725×
12,922,988×
13,010,344×
10,607,042×
12,081,671×
9,751,978×
11,392,062×
13,944,300×
10,157,590×
9,431,002×
8,811,825×
9,494,944×
11,099,827×
11,314,741×
9,930,541×
9,563,279×
8,508,807×
7,278,237×
5,773,497×
5,895,489×
6,997,880×
6,418,404×
6,499,439×
6,640,194×
5,181,596×
5,545,577×
4,953,033×
5,388,086×
5,189,718×
4,667,985×
4,045,810×
2,729,035×
2,875,766×
3,940,622×
4,981,390×
4,289,387×
4,878,202×
5,203,761×
5,184,862×
5,449,585×
4,446,912×
4,386,922×
4,815,788×
5,351,371×
6,894,404×
6,110,739×
3,500,037×
3,765,031×
5,884,766×
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×