Base 70: Iteration Frequencies: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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 7 8
Average Steps
Full Cycle		1.99 step
avg		35.51 step
avg		15.77 step
avg		14.17 step
avg		18.08 step
avg		147.03 step
avg		22.58 step
avg		738.30 step
avg
Step Frequency
Full Cycle
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0×
1×
69×
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0×
1×
69×
0×
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0×
0×
0×
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0×
0×
0×
0×
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0×
0×
0×
0×
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0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
18×
1,207×
1,190×
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0×
1×
1,329×
1,258×
2,514×
2,506×
2,494×
2,478×
2,458×
2,434×
2,406×
2,374×
2,338×
2,298×
2,254×
2,206×
2,154×
2,098×
2,038×
1,974×
1,906×
1,834×
1,758×
1,678×
1,594×
1,506×
1,414×
1,318×
1,218×
1,114×
1,006×
894×
778×
658×
534×
406×
274×
138×
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0×
1×
881×
1,246×
7,260×
3,810×
15,540×
6,444×
15,696×
62,160×
4,335×
3,916×
0×
55,944×
155,232×
621,600×
66,529×
58,201×
5,823×
3,812×
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0×
1×
69×
3,708×
42,450×
100,578×
87,906×
125,858×
228,672×
295,994×
438,822×
460,878×
691,242×
585,262×
937,944×
808,316×
1,205,156×
997,806×
1,362,300×
1,071,238×
1,309,780×
962,976×
1,133,714×
740,194×
814,206×
557,616×
474,536×
302,188×
198,116×
110,470×
45,920×
12,064×
2,784×
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0×
1×
6,929×
6,216×
4,452×
0×
0×
0×
0×
0×
0×
0×
29,348×
117,328×
98,922×
79,484×
10,534×
0×
0×
0×
0×
0×
0×
0×
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0×
0×
0×
0×
0×
0×
205,119×
494,496×
427,483×
537,261×
562,211×
670,470×
681,085×
643,180×
618,201×
560,223×
646,917×
438,688×
440,462×
417,989×
378,636×
299,882×
388,955×
384,431×
347,508×
397,805×
288,128×
341,505×
527,646×
443,012×
431,716×
569,257×
519,789×
477,492×
394,929×
270,154×
355,119×
365,820×
316,878×
308,936×
325,200×
386,616×
607,650×
1,231,750×
971,871×
1,340,862×
1,602,089×
1,668,509×
1,432,518×
1,440,495×
1,460,772×
1,419,890×
1,607,916×
1,663,109×
1,746,427×
1,578,334×
1,316,172×
1,823,681×
1,746,765×
1,545,008×
1,074,897×
1,191,890×
902,072×
994,591×
1,112,351×
1,200,197×
1,695,986×
2,700,257×
2,508,698×
2,868,390×
2,868,875×
3,031,269×
2,690,363×
2,645,733×
2,685,261×
2,263,982×
2,548,803×
2,505,749×
2,698,604×
2,454,738×
2,199,854×
2,015,493×
2,145,411×
2,563,740×
2,288,420×
2,415,236×
2,297,169×
1,983,830×
2,270,266×
2,115,827×
2,059,960×
2,162,785×
2,011,244×
1,973,636×
2,161,022×
2,405,104×
2,437,022×
2,334,895×
2,745,105×
2,378,137×
2,159,115×
2,110,568×
2,363,665×
2,289,685×
2,323,342×
2,022,673×
1,905,899×
1,964,948×
1,727,758×
1,474,165×
1,837,778×
2,031,811×
1,808,843×
1,807,925×
1,640,261×
1,418,793×
1,596,661×
1,239,921×
1,080,212×
986,601×
960,714×
883,547×
761,174×
707,315×
675,971×
495,237×
417,258×
274,394×
232,515×
308,888×
292,238×
169,938×
181,104×
209,586×
210,336×
234,627×
284,028×
205,225×
141,602×
166,693×
160,572×
184,476×
189,350×
92,617×
134,139×
65,175×
66,524×
113,905×
162,846×
134,959×
95,088×
130,067×
85,936×
95,621×
64,728×
44,112×
50,930×
77,388×
69,438×
92,346×
127,434×
116,304×
142,320×
66,113×
66,400×
47,287×
68,982×
62,586×
48,702×
31,256×
77,364×
133,455×
129,955×
194,716×
195,454×
184,740×
157,105×
111,827×
148,971×
149,578×
164,287×
150,636×
186,879×
239,082×
280,049×
190,158×
206,751×
215,646×
148,660×
115,607×
126,310×
162,985×
162,340×
204,632×
206,099×
148,682×
125,031×
182,904×
138,025×
187,715×
256,769×
194,650×
211,384×
241,064×
291,270×
259,784×
240,766×
252,610×
219,832×
333,610×
282,003×
173,353×
321,022×
176,852×
193,562×
223,095×
201,719×
295,196×
317,197×
395,876×
395,551×
357,219×
433,247×
319,158×
275,322×
231,135×
308,304×
228,419×
292,244×
159,396×
127,174×
74,075×
54,835×
97,649×
107,728×
68,194×
58,478×
69,858×
116,662×
95,192×
113,064×
84,126×
49,080×
97,661×
102,944×
220,149×
162,590×
253,113×
285,934×
265,338×
286,986×
294,104×
383,734×
338,047×
352,451×
454,598×
441,398×
377,134×
324,105×
325,145×
430,631×
464,811×
410,953×
499,082×
538,259×
420,361×
386,248×
281,347×
215,975×
205,466×
188,362×
214,851×
202,066×
249,526×
264,665×
199,857×
100,072×
97,351×
103,005×
31,992×
61,968×
39,668×
46,528×
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0×
1×
69×
0×
0×
438,390×
1,142,204×
3,005,366×
3,789,560×
5,950,262×
9,108,760×
13,791,056×
20,568,362×
30,111,256×
41,386,984×
54,438,526×
72,618,046×
88,409,000×
103,775,526×
111,929,030×
139,286,166×
161,277,066×
166,823,516×
176,218,514×
181,835,748×
162,568,348×
142,894,208×
137,023,782×
115,725,714×
85,865,424×
65,096,650×
45,654,142×
25,944,810×
11,769,658×
4,953,094×
1,775,712×
959,720×
39,922×
14,808×
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0×
1×
5,669×
6,216×
4,452×
0×
0×
0×
197,424×
717,570×
350,080×
682,384×
862,426×
1,326,097×
1,606,684×
1,199,488×
920,538×
2,954,954×
3,719,051×
3,137,366×
3,377,142×
2,675,777×
1,606,176×
1,708,035×
2,201,524×
2,707,616×
3,078,584×
3,610,872×
3,901,824×
3,507,881×
3,407,142×
5,244,857×
3,686,278×
2,461,030×
2,792,625×
3,093,878×
2,556,925×
2,311,271×
3,628,743×
4,908,290×
6,835,427×
5,191,516×
5,655,238×
6,516,805×
4,555,185×
4,672,857×
3,514,777×
4,079,370×
4,567,475×
4,880,132×
5,221,486×
5,268,467×
4,425,226×
2,918,700×
2,483,491×
3,992,544×
3,203,233×
4,417,153×
7,249,824×
7,810,344×
6,463,680×
6,332,664×
7,536,874×
6,530,271×
6,833,166×
4,912,624×
5,217,063×
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6,487,321×
4,636,262×
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6,169,726×
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5,041,708×
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4,224,230×
3,437,241×
3,669,125×
4,524,742×
3,874,190×
5,370,157×
6,132,670×
5,205,158×
3,515,866×
4,769,471×
2,783,053×
3,705,165×
5,701,551×
8,102,989×
7,415,285×
6,388,903×
4,690,359×
3,798,736×
3,853,951×
4,028,313×
4,057,462×
4,023,051×
5,438,139×
5,086,175×
3,970,026×
4,113,216×
3,174,340×
4,626,266×
6,177,430×
6,688,509×
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4,971,312×
4,678,580×
4,628,102×
3,423,559×
4,871,264×
5,201,992×
4,994,777×
5,853,514×
7,378,025×
8,190,699×
7,900,246×
8,054,386×
8,322,018×
8,626,498×
7,177,946×
8,211,174×
8,672,829×
10,839,818×
11,574,746×
12,582,358×
13,019,180×
11,401,299×
10,418,245×
10,303,178×
13,100,945×
16,237,370×
15,990,192×
16,995,501×
15,851,233×
14,021,765×
12,725,806×
10,474,317×
9,410,385×
9,878,883×
9,578,638×
10,243,166×
9,733,800×
10,595,886×
9,815,372×
9,595,448×
9,027,617×
7,999,339×
5,532,992×
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3,776,021×
4,264,404×
5,137,584×
4,903,028×
5,021,511×
3,972,947×
4,633,608×
5,633,095×
8,990,108×
10,984,307×
7,946,302×
7,374,473×
5,653,655×
4,671,377×
3,013,486×
4,874,396×
4,342,275×
3,936,023×
4,405,561×
4,093,601×
3,588,259×
2,985,238×
3,135,562×
2,852,079×
2,818,828×
2,598,836×
1,385,000×
1,369,944×
1,962,161×
2,430,096×
3,219,138×
3,253,937×
3,307,144×
3,407,027×
2,905,874×
3,927,730×
4,700,906×
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5,606,350×
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3,515,178×
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4,031,170×
4,026,118×
3,773,806×
3,083,045×
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2,295,116×
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1,896,974×
1,138,009×
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953,902×
1,290,034×
386,694×
574,421×
930,737×
261,963×
212,624×
42,952×
256,932×
249,732×
614,334×
439,393×
250,012×
296,811×
191,792×
38,772×
223,030×
78,390×
19,430×
0×
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10,920,098×
51,429,679×
43,503,101×
51,458,277×
52,067,663×
51,374,085×
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