Base 116: 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		23.41 step
avg		4.07 step
avg		22.44 step
avg		190.30 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
115×
0s:
1s:
2s:
30×
3,450×
3,306×
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1×
3,537×
3,420×
6,838×
6,830×
6,818×
6,802×
6,782×
6,758×
6,730×
6,698×
6,662×
6,622×
6,578×
6,530×
6,478×
6,422×
6,362×
6,298×
6,230×
6,158×
6,082×
6,002×
5,918×
5,830×
5,738×
5,642×
5,542×
5,438×
5,330×
5,218×
5,102×
4,982×
4,858×
4,730×
4,598×
4,462×
4,322×
4,178×
4,030×
3,878×
3,722×
3,562×
3,398×
3,230×
3,058×
2,882×
2,702×
2,518×
2,330×
2,138×
1,942×
1,742×
1,538×
1,330×
1,118×
902×
682×
458×
230×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
1×
120,235×
316,316×
1,266,720×
5,066,880×
305,760×
272,423×
504,176×
28,034×
22,012×
38,194×
0s:
1s:
2s:
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45s:
1×
253,467×
257,838×
350,942×
768,668×
1,086,660×
1,680,754×
1,865,998×
2,717,852×
2,367,142×
4,090,282×
3,389,142×
5,341,080×
3,886,668×
6,596,048×
4,413,356×
7,878,784×
5,645,564×
9,359,054×
7,539,994×
10,196,084×
8,074,324×
9,849,060×
7,629,638×
9,172,962×
6,954,698×
8,936,814×
6,290,318×
7,815,726×
5,884,960×
6,486,032×
5,222,080×
5,265,156×
4,358,282×
4,067,792×
3,466,378×
2,962,966×
2,505,266×
1,953,330×
1,476,976×
967,758×
678,154×
460,400×
280,202×
126,536×
6,838×
0s:
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536s:
537s:
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539s:
540s:
541s:
542s:
543s:
544s:
545s:
546s:
1×
4,218,153×
11,259,550×
7,747,182×
9,956,674×
12,916,048×
16,631,840×
17,581,662×
19,138,744×
18,776,849×
19,940,710×
19,631,807×
19,712,246×
18,906,452×
20,337,350×
20,698,941×
20,582,465×
22,322,540×
19,711,632×
16,372,311×
16,572,657×
16,035,701×
16,161,716×
16,217,985×
18,624,141×
18,381,461×
19,386,630×
20,142,098×
19,131,026×
19,768,042×
18,700,505×
18,174,525×
17,894,274×
16,653,899×
14,083,777×
13,487,078×
13,624,435×
13,649,408×
13,519,495×
14,267,075×
13,233,151×
15,223,967×
14,413,469×
13,679,380×
12,986,471×
14,706,594×
14,018,811×
11,425,284×
10,698,979×
11,214,262×
11,650,673×
11,196,393×
11,000,398×
11,231,280×
11,647,708×
11,113,642×
11,834,644×
9,691,318×
10,324,739×
10,656,896×
10,391,451×
9,362,804×
9,148,086×
8,174,331×
7,812,575×
8,490,582×
9,145,801×
10,532,262×
10,482,532×
11,213,959×
11,631,095×
12,188,075×
12,981,642×
13,033,689×
12,406,655×
13,393,017×
14,703,981×
14,002,897×
16,275,073×
16,653,350×
15,780,569×
15,228,362×
17,284,849×
16,726,587×
16,427,261×
16,611,875×
15,156,703×
15,677,675×
15,294,781×
13,384,432×
13,335,826×
14,833,559×
15,421,695×
14,968,760×
14,385,270×
14,691,527×
13,609,431×
13,023,172×
12,969,679×
13,479,963×
13,290,515×
12,268,753×
10,476,904×
8,853,870×
9,534,071×
10,426,523×
9,902,900×
9,362,765×
8,297,355×
8,411,786×
8,482,669×
8,193,469×
8,532,562×
7,606,479×
6,986,599×
6,763,947×
4,677,737×
5,343,000×
4,606,295×
4,310,750×
5,028,009×
4,148,346×
3,948,972×
4,062,833×
4,854,295×
5,073,860×
4,641,361×
4,080,336×
5,206,948×
5,611,903×
7,008,193×
6,815,038×
5,945,724×
4,475,283×
5,466,834×
5,292,784×
4,663,011×
4,779,422×
4,832,726×
4,959,612×
5,232,539×
4,835,568×
5,159,340×
4,813,931×
4,575,644×
5,343,528×
5,181,272×
5,327,560×
5,348,878×
3,680,858×
3,284,470×
3,336,150×
3,490,506×
3,026,076×
3,268,952×
4,320,289×
3,592,639×
3,299,314×
4,123,518×
4,474,313×
4,820,214×
3,478,968×
2,828,354×
2,605,541×
2,986,518×
3,260,944×
2,520,836×
2,469,827×
2,744,094×
2,782,754×
3,009,774×
3,335,498×
3,041,124×
2,708,466×
2,906,343×
2,854,046×
2,408,685×
2,378,291×
2,638,059×
3,093,727×
2,634,333×
2,005,740×
2,295,840×
1,806,882×
1,961,260×
2,204,356×
2,322,018×
2,274,126×
2,464,050×
2,493,194×
2,790,878×
3,018,004×
2,590,114×
3,297,236×
3,680,980×
3,492,210×
4,566,114×
6,159,837×
5,675,006×
5,784,456×
5,971,779×
7,604,166×
6,492,653×
7,537,850×
7,439,561×
7,487,484×
8,792,821×
9,024,228×
9,249,327×
10,957,607×
10,426,567×
11,338,064×
9,901,774×
10,475,810×
10,373,262×
9,404,655×
10,523,406×
9,844,189×
9,362,765×
9,696,668×
11,262,409×
11,792,842×
11,734,426×
10,703,015×
11,827,830×
11,015,531×
10,891,837×
11,120,119×
11,614,610×
12,480,828×
11,323,129×
11,138,091×
12,456,867×
12,407,557×
12,558,939×
11,284,822×
12,901,210×
11,985,607×
10,921,381×
11,528,854×
10,659,112×
11,083,676×
11,505,746×
11,882,505×
12,119,835×
11,772,840×
13,698,778×
13,568,416×
13,125,884×
13,491,010×
12,432,687×
12,900,581×
11,779,376×
12,257,046×
12,283,639×
13,198,551×
13,915,487×
14,261,977×
14,227,388×
13,327,183×
13,288,326×
12,656,051×
12,652,652×
11,945,831×
11,672,766×
11,386,587×
10,463,526×
11,460,405×
11,259,942×
11,352,367×
11,990,572×
11,226,972×
10,530,128×
11,725,459×
13,073,007×
14,749,605×
14,278,257×
14,059,823×
12,418,552×
12,428,850×
14,195,456×
12,484,862×
14,776,822×
14,338,459×
12,567,116×
12,504,292×
12,023,329×
11,309,375×
11,626,057×
11,139,295×
10,863,352×
10,232,091×
11,869,709×
11,339,320×
10,799,247×
12,656,392×
11,965,378×
11,416,282×
12,381,873×
12,739,992×
13,045,272×
11,592,556×
11,368,357×
9,055,748×
8,213,081×
9,269,649×
9,220,861×
9,840,625×
8,733,306×
8,216,161×
7,993,663×
7,957,423×
8,642,309×
8,339,481×
7,553,210×
6,780,520×
7,154,652×
7,259,853×
6,093,818×
6,960,743×
5,403,211×
5,580,290×
5,214,598×
4,102,652×
5,000,510×
4,378,216×
3,998,013×
3,884,224×
4,003,250×
3,956,770×
4,624,874×
3,458,650×
3,374,800×
3,716,736×
3,670,743×
4,477,134×
4,516,514×
4,051,271×
3,765,328×
4,246,322×
4,587,742×
3,958,860×
3,450,588×
4,504,941×
4,681,415×
5,176,518×
4,096,288×
3,548,515×
3,528,427×
4,243,043×
3,820,698×
4,286,373×
3,821,167×
3,663,336×
3,831,165×
3,955,160×
3,327,744×
3,682,423×
2,456,439×
2,141,756×
2,938,006×
1,790,032×
1,707,420×
1,263,014×
1,283,968×
1,197,872×
1,313,164×
1,735,533×
1,727,440×
2,156,118×
1,960,230×
2,549,066×
2,034,533×
2,233,341×
2,080,827×
2,146,704×
2,610,086×
2,910,636×
2,194,916×
2,775,972×
2,192,070×
2,389,866×
2,652,204×
2,050,891×
1,944,069×
1,399,470×
1,746,756×
2,225,656×
2,419,416×
2,344,393×
2,274,550×
2,131,949×
2,958,112×
3,131,558×
4,231,199×
2,807,232×
3,241,216×
3,625,393×
4,004,431×
3,902,496×
4,494,784×
4,083,221×
3,601,448×
4,473,066×
3,806,906×
3,207,710×
3,408,290×
2,984,364×
3,773,635×
3,148,158×
3,701,093×
3,937,935×
3,873,232×
3,877,171×
4,799,811×
5,245,733×
4,240,375×
3,952,282×
3,095,380×
4,680,454×
4,640,304×
5,382,526×
5,531,743×
5,622,852×
5,902,358×
6,286,646×
6,147,248×
6,019,948×
6,924,818×
5,696,923×
5,915,946×
5,216,451×
4,753,766×
3,561,536×
3,745,390×
4,921,332×
3,862,872×
3,581,130×
3,398,402×
2,986,985×
3,670,521×
3,373,670×
4,081,142×
3,367,016×
3,026,963×
2,647,980×
2,619,203×
2,837,879×
3,545,458×
3,850,360×
3,465,750×
2,400,072×
2,485,458×
2,041,645×
1,517,206×
1,905,560×
1,687,806×
1,644,839×
1,174,734×
1,251,416×
1,449,483×
1,611,730×
1,308,908×
1,294,290×
1,607,438×
1,466,756×
1,782,202×
2,159,142×
1,860,148×
2,171,446×
2,405,684×
3,002,786×
2,845,978×
3,104,109×
2,273,925×
2,819,018×
2,224,832×
2,054,206×
2,928,892×
1,977,440×
2,283,359×
2,195,079×
2,076,190×
2,624,769×
1,801,492×
1,921,716×
2,246,010×
2,365,719×
2,503,200×
1,887,044×
1,899,510×
1,908,448×
1,773,999×
2,214,884×
1,938,331×
2,025,138×
1,379,231×
1,556,348×
1,783,146×
1,195,284×
1,450,242×
1,019,188×
919,344×
853,578×
1,044,332×
1,248,824×
983,100×
765,624×
1,039,058×
1,201,859×
889,568×
1,183,827×
1,014,409×
1,872,638×
1,681,176×
1,756,448×
1,878,342×
974,202×
1,341,946×
1,531,842×
1,273,348×
1,432,246×
1,634,562×
1,447,736×
1,276,474×
1,168,618×
1,317,302×
969,696×
784,842×
901,794×
745,578×
898,229×
647,502×
355,348×
373,028×
604,676×
370,006×
477,160×
631,172×
712,225×
504,524×
659,416×
705,948×
668,024×
279,928×
294,228×
68,226×