Base 114: 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		23.03 step
avg		2.83 step
avg		24.48 step
avg		179.66 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
113×
0s:
1s:
2s:
30×
3,333×
3,192×
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1×
3,419×
3,304×
6,606×
6,598×
6,586×
6,570×
6,550×
6,526×
6,498×
6,466×
6,430×
6,390×
6,346×
6,298×
6,246×
6,190×
6,130×
6,066×
5,998×
5,926×
5,850×
5,770×
5,686×
5,598×
5,506×
5,410×
5,310×
5,206×
5,098×
4,986×
4,870×
4,750×
4,626×
4,498×
4,366×
4,230×
4,090×
3,946×
3,798×
3,646×
3,490×
3,330×
3,166×
2,998×
2,826×
2,650×
2,470×
2,286×
2,098×
1,906×
1,710×
1,510×
1,306×
1,098×
886×
670×
450×
226×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
1×
453,209×
1,270,836×
5,084,856×
307,683×
270,461×
15,129×
11,530×
0s:
1s:
2s:
3s:
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44s:
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48s:
1×
67,713×
77,942×
132,002×
283,562×
475,038×
811,416×
1,040,970×
1,497,206×
1,425,270×
2,572,892×
2,484,666×
3,696,350×
2,953,892×
4,855,134×
3,418,964×
6,024,308×
4,109,052×
7,357,514×
5,465,314×
8,455,548×
6,359,786×
8,902,024×
6,689,480×
8,818,448×
6,913,142×
9,067,654×
6,492,088×
8,184,360×
6,000,800×
7,281,846×
5,438,756×
6,299,762×
4,618,272×
5,092,944×
4,031,836×
3,888,038×
3,169,562×
2,882,404×
2,245,130×
1,797,818×
1,357,294×
1,018,446×
676,742×
352,424×
139,566×
34,660×
5,176×
226×
0s:
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633s:
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636s:
637s:
1×
3,216,354×
8,543,831×
8,169,152×
11,371,430×
13,166,122×
14,322,843×
13,113,456×
13,588,229×
12,849,343×
13,091,990×
13,299,547×
12,586,856×
12,733,574×
11,925,254×
12,749,799×
14,145,039×
14,298,245×
15,163,014×
15,218,679×
14,674,862×
14,466,781×
14,871,833×
15,200,485×
16,186,048×
17,432,014×
16,628,737×
16,923,481×
16,838,505×
15,730,526×
18,130,829×
16,970,487×
17,555,991×
17,301,546×
17,162,071×
18,445,499×
20,441,933×
22,419,769×
22,482,231×
22,096,693×
20,210,744×
19,124,414×
20,709,996×
20,151,358×
20,113,186×
20,714,879×
19,061,783×
17,478,375×
18,294,329×
20,769,116×
21,539,629×
19,328,410×
18,713,470×
18,714,963×
17,673,682×
17,617,809×
16,696,201×
17,738,545×
17,787,049×
16,062,992×
15,573,984×
16,359,387×
14,802,694×
16,113,189×
15,758,451×
15,741,216×
15,312,570×
15,364,783×
14,047,353×
14,243,469×
13,268,397×
12,331,205×
11,407,362×
11,169,630×
11,035,902×
11,861,650×
12,295,289×
11,399,850×
12,420,204×
11,552,950×
12,472,565×
11,715,667×
11,796,067×
11,417,267×
12,111,552×
11,180,109×
10,562,603×
10,337,409×
10,239,511×
10,450,489×
11,329,870×
9,488,386×
10,920,715×
10,167,371×
9,217,220×
10,464,900×
10,766,983×
11,190,626×
11,126,837×
11,018,404×
10,118,710×
10,152,069×
11,318,892×
11,778,528×
12,480,181×
12,997,240×
13,048,855×
13,038,295×
12,656,003×
12,237,811×
11,471,970×
10,717,165×
10,408,390×
10,704,825×
9,729,645×
9,435,381×
10,885,500×
10,009,686×
9,535,637×
9,240,319×
10,467,857×
11,232,693×
10,360,916×
11,807,308×
10,979,727×
10,972,421×
11,445,794×
9,884,002×
9,307,760×
8,974,329×
10,640,956×
11,308,013×
12,092,684×
10,887,661×
10,862,183×
9,468,174×
9,220,897×
9,298,697×
9,179,042×
9,655,346×
8,514,663×
8,546,421×
8,308,297×
10,031,375×
8,880,680×
8,082,704×
9,406,704×
9,154,749×
8,545,974×
7,527,523×
7,682,048×
6,796,769×
5,999,864×
6,043,820×
5,789,490×
6,052,906×
5,821,311×
5,441,716×
6,195,704×
4,784,831×
5,300,250×
6,094,022×
5,512,484×
5,277,632×
4,964,934×
5,930,768×
5,874,064×
5,338,091×
5,453,391×
4,925,239×
4,308,357×
4,532,321×
3,592,232×
3,164,406×
3,832,715×
4,382,053×
4,596,711×
3,963,538×
3,956,585×
3,542,032×
3,846,761×
3,588,647×
3,517,093×
2,725,321×
2,164,007×
2,352,770×
2,331,141×
1,884,858×
2,462,647×
2,285,912×
3,104,708×
2,597,168×
2,281,122×
2,441,689×
2,340,883×
2,002,848×
2,431,511×
1,957,800×
1,514,228×
1,343,958×
1,820,264×
1,871,732×
1,684,747×
2,021,668×
2,293,627×
2,707,250×
2,740,087×
3,116,106×
3,803,250×
3,084,063×
3,267,570×
4,022,669×
4,247,532×
4,379,512×
4,010,355×
4,456,573×
5,078,665×
4,325,691×
2,894,823×
2,674,882×
3,407,987×
3,724,903×
3,942,962×
4,265,208×
3,980,325×
4,886,698×
4,992,202×
4,315,514×
4,457,343×
3,885,124×
4,010,000×
3,909,919×
4,538,591×
4,693,595×
4,590,866×
4,300,548×
3,884,981×
3,110,695×
2,653,421×
2,825,754×
3,617,907×
4,723,997×
4,588,920×
4,287,773×
4,471,806×
4,045,044×
4,030,520×
5,066,291×
5,472,827×
5,368,357×
5,670,373×
6,030,796×
5,736,610×
5,550,276×
5,548,106×
6,000,549×
6,107,848×
5,624,131×
6,290,679×
6,876,275×
6,765,503×
7,014,463×
7,046,537×
7,192,700×
6,462,252×
6,579,410×
6,733,607×
6,409,367×
7,051,844×
6,758,172×
7,218,082×
7,621,435×
7,476,611×
7,416,348×
7,636,042×
7,325,695×
6,188,315×
7,079,004×
6,724,944×
6,966,143×
6,971,472×
7,008,545×
7,115,793×
6,767,285×
5,644,990×
5,841,038×
6,138,093×
6,432,168×
6,560,370×
7,081,831×
6,985,945×
7,232,378×
6,680,394×
6,958,940×
6,419,092×
6,777,632×
6,370,102×
6,980,632×
6,714,753×
6,298,938×
6,138,504×
6,318,785×
6,494,074×
5,902,309×
6,280,228×
7,056,367×
6,636,444×
5,106,672×
5,853,417×
6,046,405×
7,094,664×
7,109,879×
6,724,440×
6,282,925×
5,343,207×
5,168,853×
5,951,004×
5,277,610×
5,961,414×
6,169,968×
5,332,402×
5,373,076×
4,936,507×
4,248,122×
4,515,534×
4,879,077×
4,633,499×
4,789,206×
4,959,926×
4,839,142×
4,690,527×
4,846,877×
5,118,466×
5,026,552×
5,534,237×
5,011,708×
5,687,780×
5,976,089×
4,576,273×
5,220,254×
4,893,967×
4,465,280×
4,338,994×
4,055,056×
3,996,186×
3,833,206×
3,534,750×
3,537,166×
3,422,084×
3,225,255×
3,610,478×
4,000,919×
3,394,473×
3,265,227×
3,258,772×
3,215,174×
2,702,694×
2,560,693×
2,433,525×
2,519,184×
2,377,167×
2,281,164×
2,930,339×
2,220,162×
2,111,572×
2,521,642×
2,883,033×
2,665,165×
3,167,814×
3,211,676×
3,013,209×
2,899,530×
2,581,031×
2,783,182×
2,540,732×
2,499,054×
2,072,789×
1,980,780×
2,026,566×
2,564,284×
1,968,024×
2,306,929×
2,501,878×
2,449,353×
2,632,305×
2,196,471×
1,939,021×
1,103,580×
1,045,566×
1,048,000×
1,304,618×
837,828×
918,089×
914,512×
1,100,558×
740,386×
767,759×
728,222×
467,092×
404,746×
493,117×
807,510×
895,768×
763,368×
786,986×
960,206×
1,051,496×
991,700×
1,069,160×
901,567×
1,356,220×
1,222,373×
1,529,601×
1,390,759×
2,116,612×
2,234,293×
2,511,111×
2,286,912×
1,690,726×
1,938,879×
1,993,805×
2,216,654×
1,956,786×
2,332,797×
1,922,561×
2,017,646×
2,484,345×
3,047,113×
2,591,202×
2,954,878×
3,300,813×
3,894,242×
3,367,645×
3,914,579×
3,004,793×
3,094,286×
2,781,047×
3,244,421×
2,869,348×
3,108,870×
1,891,712×
2,282,486×
2,681,936×
2,601,675×
2,391,914×
2,221,316×
2,664,875×
2,366,976×
2,792,720×
2,687,157×
2,990,675×
3,930,421×
3,920,544×
4,033,509×
3,632,439×
3,798,841×
3,939,954×
3,441,123×
3,652,960×
3,475,970×
4,046,390×
3,744,398×
4,013,062×
3,902,913×
3,560,554×
3,625,723×
4,483,198×
4,151,204×
4,965,715×
4,538,958×
4,139,972×
4,980,608×
5,047,482×
4,591,070×
3,921,564×
3,880,339×
2,995,707×
2,083,779×
1,960,951×
1,854,342×
1,636,855×
1,733,726×
1,640,526×
1,564,921×
1,057,150×
1,184,192×
1,095,440×
771,105×
894,590×
1,070,814×
1,128,078×
1,013,682×
919,392×
1,653,441×
1,771,865×
1,839,656×
2,439,436×
2,145,303×
2,542,848×
2,681,726×
2,302,959×
2,503,411×
2,781,958×
2,187,037×
1,371,470×
1,626,918×
2,140,784×
1,747,879×
1,745,171×
2,065,579×
2,099,364×
2,127,633×
1,949,528×
1,945,088×
1,730,601×
1,399,097×
1,514,416×
1,516,002×
1,701,282×
1,798,017×
1,545,354×
1,147,034×
1,760,124×
1,761,040×
1,756,636×
2,099,753×
2,084,806×
2,000,497×
1,396,506×
1,667,675×
1,420,450×
1,332,526×
1,367,017×
1,151,080×
1,359,620×
1,612,025×
1,104,524×
1,165,211×
1,027,342×
1,141,060×
1,232,788×
1,280,040×
1,327,870×
1,226,670×
1,843,558×
1,863,332×
1,626,250×
1,607,064×
960,544×
892,293×
752,471×
669,814×
876,156×
919,194×
1,034,027×
728,260×
696,254×
381,796×
544,910×
404,568×
424,750×
323,808×
340,755×
395,928×
483,926×
352,046×
301,314×
256,276×
320,360×
398,652×
500,038×
607,452×
752,592×
859,970×
1,011,107×
1,224,430×
1,276,196×
1,159,734×
1,419,250×
1,591,778×
801,838×
1,045,000×
1,361,821×
1,330,514×
1,358,907×
1,989,104×
1,258,328×
1,346,263×
1,798,624×
1,283,429×
1,237,415×
1,089,638×
966,528×
1,111,343×
1,040,542×
1,121,287×
1,455,770×
1,416,574×
1,707,640×
1,552,088×
1,475,270×
1,743,084×
1,391,327×
992,762×
533,589×
761,422×
627,778×
749,846×
671,292×
636,521×
598,888×
721,934×
749,772×
650,523×
331,584×
268,684×
293,926×
401,472×
466,614×
831,386×
699,957×
701,847×
471,460×
391,606×
73,968×
172,200×
307,938×
288,308×
236,382×
301,188×
151,516×
157,133×
56,388×
11,238×
10,134×
8,718×
7,794×
228×