Base 126: 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		1.48 step
avg		25.29 step
avg		2.82 step
avg		26.63 step
avg		164.28 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
125×
0s:
1s:
2s:
33×
4,062×
3,906×
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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×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
1×
674,685×
1,903,710×
7,616,700×
415,670×
368,143×
18,423×
12,044×
0s:
1s:
2s:
3s:
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47s:
48s:
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50s:
51s:
1×
89,751×
102,316×
175,466×
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×
0s:
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486s:
487s:
1×
15,069,969×
44,309,212×
15,229,369×
15,099,166×
17,046,289×
18,844,677×
18,944,890×
18,711,502×
22,282,191×
24,806,461×
24,057,945×
22,655,024×
20,007,672×
22,475,678×
25,668,044×
26,190,522×
22,519,684×
22,418,204×
26,800,015×
28,625,328×
30,721,709×
31,140,873×
29,332,616×
26,623,922×
27,655,024×
29,630,494×
28,282,169×
27,380,741×
25,456,511×
22,426,587×
20,310,771×
19,649,091×
18,710,282×
19,223,889×
20,788,930×
24,737,793×
22,795,038×
25,934,673×
23,918,804×
25,511,972×
26,242,468×
24,155,710×
25,436,188×
28,069,985×
24,874,541×
25,262,351×
23,564,765×
26,255,059×
30,591,600×
31,363,931×
30,317,020×
28,323,525×
30,545,648×
33,429,081×
28,014,013×
26,375,317×
27,973,691×
23,958,378×
24,837,437×
26,439,795×
25,711,609×
27,288,583×
29,656,836×
27,913,425×
28,505,670×
28,057,126×
31,159,855×
29,783,292×
27,811,407×
26,052,750×
22,807,116×
20,774,092×
22,948,384×
24,290,341×
24,473,829×
23,400,222×
23,824,281×
22,803,603×
24,671,403×
25,615,090×
24,617,645×
22,681,411×
23,525,355×
22,475,496×
18,179,298×
19,165,145×
18,213,542×
20,200,272×
21,888,619×
21,970,991×
19,145,926×
17,920,726×
18,798,972×
19,018,468×
20,234,374×
18,059,645×
19,674,752×
19,512,016×
19,600,461×
19,561,491×
20,087,347×
17,959,989×
15,248,440×
14,892,434×
16,401,194×
16,875,410×
16,150,156×
16,186,703×
16,795,358×
17,302,388×
15,711,227×
17,560,116×
17,789,500×
14,554,491×
15,434,143×
13,859,157×
14,019,281×
14,097,921×
13,808,061×
13,747,335×
13,605,669×
13,711,627×
15,410,042×
15,273,221×
15,704,899×
17,969,568×
18,939,389×
21,568,836×
22,716,918×
21,581,272×
21,221,178×
20,613,103×
19,342,416×
18,864,740×
16,662,962×
17,984,562×
18,679,884×
18,859,298×
17,305,735×
14,326,082×
14,482,680×
17,600,564×
20,013,947×
19,342,006×
20,559,140×
19,357,533×
20,117,236×
19,828,133×
21,597,021×
21,942,171×
20,983,893×
19,108,511×
19,513,126×
18,223,777×
19,335,444×
17,559,751×
18,803,341×
20,448,935×
20,966,018×
21,164,313×
21,349,224×
21,689,484×
21,296,855×
20,965,372×
18,132,542×
16,381,423×
15,177,517×
15,369,218×
14,869,925×
14,277,891×
13,243,033×
12,938,260×
11,144,969×
10,069,015×
10,638,320×
10,592,147×
11,673,655×
11,438,408×
12,247,589×
10,890,174×
12,704,801×
12,833,839×
14,238,340×
15,584,103×
12,859,535×
12,956,153×
12,530,246×
12,776,251×
12,624,051×
14,085,414×
17,072,507×
16,069,421×
14,974,438×
14,843,416×
14,546,396×
13,441,732×
11,682,654×
13,491,811×
15,055,501×
14,280,130×
12,910,404×
14,638,693×
13,796,737×
14,474,217×
15,345,191×
15,023,728×
14,108,801×
14,255,106×
15,100,506×
15,048,644×
13,516,643×
13,747,039×
12,364,580×
14,754,921×
13,292,458×
10,405,380×
10,369,695×
10,515,675×
11,729,613×
11,507,169×
12,186,109×
11,728,044×
12,421,990×
9,779,497×
11,378,304×
9,277,352×
9,461,563×
10,830,875×
11,367,239×
11,871,465×
10,370,194×
9,237,346×
8,012,360×
9,161,701×
9,520,499×
9,626,376×
8,567,347×
9,482,375×
10,314,925×
9,838,676×
12,068,533×
12,100,446×
13,980,364×
13,209,422×
11,576,292×
12,911,857×
12,892,289×
15,306,393×
15,508,117×
14,951,637×
13,624,299×
12,690,228×
15,400,374×
17,156,200×
17,475,430×
18,637,709×
19,368,783×
18,355,954×
17,899,609×
16,886,617×
17,324,420×
18,170,378×
17,338,562×
17,199,854×
18,075,734×
16,789,513×
17,199,794×
20,229,955×
23,277,657×
21,575,980×
19,083,363×
19,583,512×
17,367,583×
17,649,728×
18,391,126×
17,541,898×
16,202,976×
14,865,406×
14,436,857×
13,634,934×
15,448,557×
16,409,856×
14,332,916×
16,402,354×
15,107,601×
14,197,965×
13,939,880×
15,167,402×
14,912,939×
15,977,013×
15,460,687×
12,937,528×
11,987,736×
11,517,854×
10,418,230×
9,588,602×
9,546,119×
8,471,576×
8,514,797×
6,816,084×
6,140,656×
5,497,061×
5,004,144×
3,953,688×
5,027,696×
4,385,943×
3,790,495×
3,852,084×
4,206,552×
5,013,527×
4,383,913×
4,162,710×
3,278,823×
4,264,038×
5,956,000×
5,148,522×
5,903,987×
4,810,687×
3,662,778×
4,112,782×
4,696,747×
3,262,270×
3,252,831×
3,589,268×
3,340,811×
3,228,696×
3,725,314×
3,800,688×
4,001,637×
3,644,731×
3,054,636×
2,622,932×
2,761,297×
3,255,244×
3,258,124×
4,235,377×
4,178,838×
4,272,670×
4,309,308×
4,255,213×
4,761,579×
4,930,935×
5,634,288×
5,400,142×
5,482,389×
5,651,470×
5,139,391×
4,102,063×
5,164,983×
4,598,934×
4,671,332×
4,968,276×
5,855,421×
6,659,315×
6,097,527×
7,371,974×
6,730,862×
7,123,073×
9,437,953×
8,234,204×
5,755,954×
5,609,907×
4,516,664×
3,788,241×
3,851,670×
3,118,364×
3,771,290×
3,338,587×
2,857,673×
3,122,230×
3,582,645×
4,095,502×
3,899,206×
4,327,534×
4,912,290×
4,671,496×
4,457,525×
3,815,862×
3,271,935×
3,783,055×
3,748,093×
4,421,079×
3,251,470×
3,694,716×
4,695,407×
5,257,693×
4,506,776×
3,082,602×
3,872,155×
3,179,386×
3,438,948×
3,617,565×
2,717,153×
2,232,991×
3,352,080×
3,540,772×
2,750,347×
1,880,235×
2,089,346×
2,462,027×
2,601,640×
3,837,076×
2,690,285×
2,803,462×
2,912,431×
3,225,883×
3,390,981×
4,126,733×
2,787,676×
2,399,323×
2,319,988×
2,958,848×
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×