Base 123: 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		7.91 step
avg		26.22 step
avg		20.51 step
avg		27.08 step
avg		255.54 step
avg
Step Frequency
Full Cycle
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122×
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1×
122×
61×
122×
8×
937×
885×
1,830×
3,660×
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0×
1×
122×
7,687×
3,840×
7,678×
7,668×
7,654×
7,636×
7,614×
7,588×
7,558×
7,524×
7,486×
7,444×
7,398×
7,348×
7,294×
7,236×
7,174×
7,108×
7,038×
6,964×
6,886×
6,804×
6,718×
6,628×
6,534×
6,436×
6,334×
6,228×
6,118×
6,004×
5,886×
5,764×
5,638×
5,508×
5,374×
5,236×
5,094×
4,948×
4,798×
4,644×
4,486×
4,324×
4,158×
3,988×
3,814×
3,636×
3,454×
3,268×
3,078×
2,884×
2,686×
2,484×
2,278×
2,068×
1,854×
1,636×
1,414×
1,188×
958×
724×
486×
244×
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0×
1×
122×
0×
0×
0×
14,280×
39,030×
0×
0×
0×
316,192×
875,914×
1,803×
0×
0×
0×
0×
0×
0×
0×
2,127,828×
6,386,146×
243,966×
3,843×
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0×
1×
72,446×
91,967×
163,826×
350,714×
588,924×
1,002,240×
1,289,808×
1,845,824×
1,765,806×
3,173,660×
3,077,727×
4,560,470×
3,664,355×
5,997,834×
4,250,861×
7,458,440×
4,880,152×
8,971,064×
6,048,277×
10,694,488×
7,867,848×
11,932,280×
8,778,397×
12,246,828×
9,191,969×
12,178,595×
9,235,105×
12,170,346×
8,635,645×
11,128,482×
8,047,017×
9,831,200×
7,489,104×
8,773,967×
6,386,059×
7,196,167×
5,696,832×
5,599,342×
4,554,281×
4,242,622×
3,387,458×
2,919,460×
2,219,549×
1,762,168×
1,283,649×
826,266×
450,528×
191,078×
55,661×
4,988×
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0×
1×
122×
0×
27,344×
145,698×
1,025,791×
2,421,525×
7,450,610×
30,726,006×
9,263,235×
6,533,466×
5,045,797×
4,245,631×
5,774,944×
4,937,115×
2,986,836×
3,583,365×
4,103,453×
3,306,471×
3,584,226×
2,689,305×
1,947,578×
1,656,763×
2,038,693×
924,896×
1,858,141×
2,658,800×
2,969,377×
2,955,629×
1,712,613×
1,409,075×
836,720×
128,021×
170,710×
783,235×
2,102,161×
3,869,604×
8,532,362×
3,467,741×
4,989,021×
4,096,916×
4,290,559×
3,930,524×
5,258,779×
4,119,524×
2,532,465×
2,344,485×
2,401,994×
2,512,713×
3,913,205×
2,240,980×
2,077,001×
3,806,102×
4,721,302×
4,608,517×
4,983,168×
4,453,279×
4,693,827×
4,430,910×
2,740,235×
2,059,809×
3,200,903×
3,870,080×
4,827,905×
4,447,071×
4,026,684×
4,013,324×
6,250,302×
6,343,199×
5,241,963×
5,756,952×
5,337,139×
6,374,871×
6,721,020×
5,708,023×
5,950,859×
4,745,170×
4,641,881×
5,288,155×
6,142,951×
6,543,077×
7,369,349×
12,233,852×
13,145,683×
13,401,067×
15,247,155×
14,905,038×
13,611,432×
9,187,314×
10,248,259×
12,658,352×
13,340,758×
13,344,159×
13,243,936×
13,110,247×
15,701,634×
13,320,006×
13,270,013×
13,750,926×
16,644,162×
13,726,476×
13,938,081×
12,598,038×
12,351,762×
11,084,013×
9,820,581×
13,800,349×
11,162,742×
9,524,131×
11,703,123×
10,936,413×
11,336,781×
13,730,109×
14,390,709×
14,477,013×
14,069,235×
12,862,288×
11,897,353×
12,351,912×
17,834,188×
19,494,647×
17,819,610×
19,536,971×
20,923,566×
21,165,037×
22,308,402×
22,938,315×
18,590,605×
17,495,726×
18,750,876×
20,499,739×
23,529,193×
19,875,860×
17,754,391×
18,148,341×
17,186,006×
16,357,410×
13,881,221×
16,112,377×
16,446,910×
12,629,862×
11,963,551×
14,085,703×
13,746,155×
13,557,293×
15,001,777×
14,777,755×
17,954,064×
22,235,805×
19,200,173×
19,014,410×
17,426,277×
16,801,147×
19,183,943×
15,074,617×
14,359,809×
16,153,338×
20,847,142×
20,515,836×
16,629,146×
17,058,379×
14,615,490×
13,726,861×
13,603,020×
14,660,385×
13,511,983×
13,360,910×
13,663,668×
12,431,667×
11,033,225×
10,574,926×
11,537,849×
12,393,496×
9,920,632×
9,126,976×
7,414,354×
8,011,338×
9,806,997×
11,953,094×
11,050,232×
12,779,171×
12,266,239×
12,383,757×
14,141,433×
13,906,039×
12,791,807×
11,301,966×
11,621,412×
10,472,508×
10,199,519×
11,294,755×
10,707,731×
11,845,067×
10,435,642×
8,530,438×
10,726,080×
10,722,360×
9,336,226×
10,887,363×
11,692,370×
13,249,015×
10,728,044×
10,503,504×
8,720,550×
8,303,867×
7,636,011×
8,044,614×
8,857,734×
10,843,348×
11,475,542×
10,522,010×
9,307,975×
9,608,524×
9,953,270×
7,854,870×
8,027,432×
9,529,149×
13,168,439×
16,045,851×
14,344,445×
12,283,879×
12,469,368×
13,191,447×
13,229,634×
12,566,878×
10,972,070×
9,229,402×
11,101,267×
11,882,174×
10,088,709×
9,219,902×
11,207,337×
10,958,659×
13,216,732×
13,654,035×
13,245,072×
13,796,062×
17,295,733×
14,434,491×
11,646,085×
11,644,129×
11,261,570×
13,878,833×
13,767,278×
14,622,822×
17,141,897×
14,553,886×
10,761,541×
12,076,019×
15,010,754×
12,590,009×
16,239,230×
17,788,921×
17,356,021×
19,052,690×
19,026,757×
14,966,549×
13,553,650×
16,693,357×
12,686,671×
16,407,646×
16,694,434×
16,149,655×
14,845,152×
15,147,068×
14,419,507×
12,050,401×
16,473,991×
18,007,752×
17,672,908×
18,874,284×
19,655,078×
17,509,636×
17,720,183×
17,714,546×
20,473,297×
20,844,952×
20,616,693×
19,074,148×
22,758,128×
22,457,280×
20,509,417×
17,978,872×
21,619,001×
24,831,341×
22,515,482×
21,180,563×
24,540,961×
23,171,173×
24,461,697×
26,302,013×
23,670,571×
20,445,784×
19,652,424×
20,713,068×
21,567,419×
21,599,692×
19,965,440×
20,139,315×
20,275,405×
18,388,676×
20,508,613×
21,864,570×
18,596,157×
17,945,145×
21,439,952×
25,404,106×
23,098,311×
19,043,716×
17,043,834×
17,865,097×
17,148,941×
17,312,845×
20,082,412×
15,925,587×
15,707,534×
14,426,766×
14,795,907×
16,168,136×
14,585,171×
12,990,079×
13,551,573×
13,967,139×
13,756,926×
9,954,410×
14,010,364×
10,500,110×
9,033,164×
12,281,288×
14,618,644×
14,230,986×
10,577,303×
10,589,925×
9,630,613×
9,402,329×
9,360,694×
9,781,819×
14,699,024×
15,589,565×
15,343,185×
16,868,734×
17,020,005×
17,271,751×
12,249,808×
12,258,323×
13,342,806×
14,695,347×
14,046,594×
12,905,693×
11,254,514×
13,411,349×
10,648,179×
13,231,641×
12,943,156×
11,796,193×
11,580,987×
12,875,742×
11,904,944×
14,208,475×
14,132,760×
14,825,919×
13,010,930×
9,634,113×
7,682,964×
6,216,159×
5,339,693×
5,870,636×
3,254,707×
2,690,678×
2,592,992×
1,616,366×
936,730×
1,311,493×
847,563×
1,807,867×
878,549×
822,387×
2,553,055×
4,653,460×
5,703,748×
4,372,957×
4,646,051×
5,514,577×
5,350,292×
4,654,421×
4,529,858×
4,238,414×
2,653,310×
2,774,577×
2,054,634×
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2,426,171×
1,857,236×
3,417,052×
5,190,836×
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6,035,851×
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6,348,583×
6,953,460×
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8,030,660×
7,064,521×
7,886,658×
8,222,378×
6,966,328×
6,414,901×
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6,191,499×
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6,048,250×
6,770,741×
6,856,297×
6,360,557×
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6,562,821×
6,045,612×
5,336,494×
5,620,660×
7,411,497×
6,555,282×
8,788,295×
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5,465,596×
8,254,357×
7,799,255×
8,962,418×
10,566,270×
10,496,261×
10,288,895×
8,271,887×
9,771,172×
10,917,080×
10,112,751×
13,311,041×
10,601,389×
11,260,126×
8,329,462×
7,771,376×
7,039,265×
6,042,592×
5,027,254×
4,538,405×
5,643,675×
6,958,875×
7,483,730×
7,310,227×
6,586,608×
7,726,091×
8,715,731×
8,134,984×
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9,139,913×
7,782,162×
8,191,017×
7,365,589×
6,585,455×
5,837,779×
5,652,177×
5,279,447×
5,368,283×
3,261,044×
2,347,767×
2,543,086×
4,088,399×
4,383,135×
2,950,647×
921,389×
828,167×
2,384,672×
3,400,117×
2,381,663×
1,772,882×
2,046,625×
1,529,301×
1,615,818×
1,348,280×
1,953,264×
1,776,098×
1,906,076×
1,520,796×
2,780,863×
2,584,642×
2,132,497×
3,370,086×
4,575,568×
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2,579,396×
2,999,591×
2,992,033×
2,019,352×
3,414,157×
2,208,518×
1,816,524×
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3,806,342×
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1,455,450×
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2,482,611×
2,416,130×
2,159,305×
4,485,248×
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2,960,782×
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1,056,122×
802,428×
1,488,528×
830,201×
715,999×
614,353×
1,548,441×
3,985,103×
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2,955,545×
4,714,190×
5,654,857×
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6,187,829×
6,216,869×
6,043,041×
6,554,646×
5,654,830×
6,627,757×
6,470,794×
5,949,994×
4,910,404×
3,703,468×
2,547,804×
2,827,230×
2,815,836×
2,087,863×
2,081,824×
2,381,728×
3,112,688×
3,170,975×
2,176,581×
1,631,177×
738,578×
1,080,863×
1,411,049×
860,964×
432,869×
1,026,090×
688,447×
607,652×
195,397×
100,933×
226,398×
322,809×
867,391×
368,214×
394,630×
402,168×
257,664×
211,189×
133,480×
151,850×
150,147×
169,843×
18,522×
17,566×
78,915×
209,565×
99,750×
543,940×
1,414,268×
864,553×
603,752×
620,119×
189,451×
189,202×
42,632×