Base 132: Iteration Frequencies: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР
СТУФХЦЧШЩЪЫЬЭЮЯа

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		26.41 step
avg		4.02 step
avg		27.70 step
avg		202.53 step
avg
Step Frequency
Cycle Start
0s:
1s:
1×
131×
0s:
1s:
2s:
34×
4,454×
4,290×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
1×
4,553×
4,420×
8,838×
8,830×
8,818×
8,802×
8,782×
8,758×
8,730×
8,698×
8,662×
8,622×
8,578×
8,530×
8,478×
8,422×
8,362×
8,298×
8,230×
8,158×
8,082×
8,002×
7,918×
7,830×
7,738×
7,642×
7,542×
7,438×
7,330×
7,218×
7,102×
6,982×
6,858×
6,730×
6,598×
6,462×
6,322×
6,178×
6,030×
5,878×
5,722×
5,562×
5,398×
5,230×
5,058×
4,882×
4,702×
4,518×
4,330×
4,138×
3,942×
3,742×
3,538×
3,330×
3,118×
2,902×
2,682×
2,458×
2,230×
1,998×
1,762×
1,522×
1,278×
1,030×
778×
522×
262×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
1×
201,411×
538,080×
2,154,240×
8,616,960×
454,280×
405,121×
745,162×
36,126×
28,398×
53,056×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
1×
102,363×
116,186×
200,366×
427,586×
719,532×
1,220,334×
1,574,916×
2,243,240×
2,155,554×
3,858,056×
3,755,820×
5,543,426×
4,476,374×
7,296,522×
5,201,486×
9,087,656×
5,919,024×
10,888,220×
6,894,640×
12,742,936×
8,673,636×
14,827,254×
10,877,628×
16,381,214×
11,808,014×
16,313,366×
12,358,762×
16,041,586×
12,217,678×
16,044,968×
11,374,166×
14,757,682×
10,534,770×
13,323,272×
9,881,090×
11,746,372×
8,709,746×
9,974,832×
7,686,494×
7,887,206×
6,434,510×
6,198,328×
4,983,818×
4,465,348×
3,543,626×
2,856,630×
2,141,230×
1,569,574×
1,035,934×
555,304×
230,678×
65,308×
8,850×
0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
16s:
17s:
18s:
19s:
20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
81s:
82s:
83s:
84s:
85s:
86s:
87s:
88s:
89s:
90s:
91s:
92s:
93s:
94s:
95s:
96s:
97s:
98s:
99s:
100s:
101s:
102s:
103s:
104s:
105s:
106s:
107s:
108s:
109s:
110s:
111s:
112s:
113s:
114s:
115s:
116s:
117s:
118s:
119s:
120s:
121s:
122s:
123s:
124s:
125s:
126s:
127s:
128s:
129s:
130s:
131s:
132s:
133s:
134s:
135s:
136s:
137s:
138s:
139s:
140s:
141s:
142s:
143s:
144s:
145s:
146s:
147s:
148s:
149s:
150s:
151s:
152s:
153s:
154s:
155s:
156s:
157s:
158s:
159s:
160s:
161s:
162s:
163s:
164s:
165s:
166s:
167s:
168s:
169s:
170s:
171s:
172s:
173s:
174s:
175s:
176s:
177s:
178s:
179s:
180s:
181s:
182s:
183s:
184s:
185s:
186s:
187s:
188s:
189s:
190s:
191s:
192s:
193s:
194s:
195s:
196s:
197s:
198s:
199s:
200s:
201s:
202s:
203s:
204s:
205s:
206s:
207s:
208s:
209s:
210s:
211s:
212s:
213s:
214s:
215s:
216s:
217s:
218s:
219s:
220s:
221s:
222s:
223s:
224s:
225s:
226s:
227s:
228s:
229s:
230s:
231s:
232s:
233s:
234s:
235s:
236s:
237s:
238s:
239s:
240s:
241s:
242s:
243s:
244s:
245s:
246s:
247s:
248s:
249s:
250s:
251s:
252s:
253s:
254s:
255s:
256s:
257s:
258s:
259s:
260s:
261s:
262s:
263s:
264s:
265s:
266s:
267s:
268s:
269s:
270s:
271s:
272s:
273s:
274s:
275s:
276s:
277s:
278s:
279s:
280s:
281s:
282s:
283s:
284s:
285s:
286s:
287s:
288s:
289s:
290s:
291s:
292s:
293s:
294s:
295s:
296s:
297s:
298s:
299s:
300s:
301s:
302s:
303s:
304s:
305s:
306s:
307s:
308s:
309s:
310s:
311s:
312s:
313s:
314s:
315s:
316s:
317s:
318s:
319s:
320s:
321s:
322s:
323s:
324s:
325s:
326s:
327s:
328s:
329s:
330s:
331s:
332s:
333s:
334s:
335s:
336s:
337s:
338s:
339s:
340s:
341s:
342s:
343s:
344s:
345s:
346s:
347s:
348s:
349s:
350s:
351s:
352s:
353s:
354s:
355s:
356s:
357s:
358s:
359s:
360s:
361s:
362s:
363s:
364s:
365s:
366s:
367s:
368s:
369s:
370s:
371s:
372s:
373s:
374s:
375s:
376s:
377s:
378s:
379s:
380s:
381s:
382s:
383s:
384s:
385s:
386s:
387s:
388s:
389s:
390s:
391s:
392s:
393s:
394s:
395s:
396s:
397s:
398s:
399s:
400s:
401s:
402s:
403s:
404s:
405s:
406s:
407s:
408s:
409s:
410s:
411s:
412s:
413s:
414s:
415s:
416s:
417s:
418s:
419s:
420s:
421s:
422s:
423s:
424s:
425s:
426s:
427s:
428s:
429s:
430s:
431s:
432s:
433s:
434s:
435s:
436s:
437s:
438s:
439s:
440s:
441s:
442s:
443s:
444s:
445s:
446s:
447s:
448s:
449s:
450s:
451s:
452s:
453s:
454s:
455s:
456s:
457s:
458s:
459s:
460s:
461s:
462s:
463s:
464s:
465s:
466s:
467s:
468s:
469s:
470s:
471s:
472s:
473s:
474s:
475s:
476s:
477s:
478s:
479s:
480s:
481s:
482s:
483s:
484s:
485s:
486s:
487s:
488s:
489s:
490s:
491s:
492s:
493s:
494s:
495s:
496s:
497s:
498s:
499s:
500s:
501s:
502s:
503s:
504s:
505s:
506s:
507s:
508s:
509s:
510s:
511s:
512s:
513s:
514s:
515s:
516s:
517s:
518s:
519s:
520s:
521s:
522s:
523s:
524s:
525s:
526s:
527s:
528s:
529s:
530s:
531s:
532s:
533s:
534s:
535s:
536s:
537s:
538s:
539s:
540s:
541s:
542s:
543s:
544s:
545s:
546s:
547s:
548s:
549s:
550s:
1×
6,093,717×
15,333,306×
13,463,092×
16,682,571×
19,739,965×
22,838,258×
20,493,922×
23,567,571×
22,748,250×
22,828,634×
23,600,871×
23,648,369×
23,648,276×
22,920,536×
24,857,527×
23,845,669×
23,503,141×
24,050,647×
21,780,996×
21,585,749×
24,309,382×
27,190,002×
24,605,122×
24,029,005×
23,524,241×
21,795,970×
21,472,000×
24,266,173×
25,681,001×
28,683,719×
26,663,837×
24,033,097×
26,092,007×
27,739,101×
26,143,196×
28,640,010×
27,590,633×
29,030,738×
30,553,374×
31,978,311×
30,701,671×
26,175,176×
24,334,997×
26,492,053×
26,334,336×
23,576,308×
20,403,012×
20,933,096×
18,893,166×
19,964,233×
20,352,441×
19,094,340×
22,523,042×
20,239,093×
21,154,735×
18,710,813×
17,205,296×
17,096,133×
17,437,312×
16,603,035×
15,589,150×
16,010,986×
17,017,450×
18,074,861×
16,552,824×
17,020,186×
18,210,681×
16,931,405×
18,596,058×
19,219,582×
16,206,485×
15,560,571×
17,857,114×
14,478,083×
16,268,426×
18,875,166×
16,947,207×
14,999,002×
14,151,148×
16,755,172×
16,643,453×
15,514,369×
16,004,629×
17,783,030×
16,801,352×
13,710,736×
14,754,362×
17,075,411×
15,939,706×
17,744,095×
16,537,087×
16,358,813×
17,070,583×
16,535,823×
16,553,472×
17,987,505×
18,669,293×
16,538,735×
13,689,566×
10,622,050×
12,115,089×
13,435,714×
13,365,320×
13,250,888×
10,955,592×
11,600,917×
11,548,641×
12,418,657×
14,627,254×
14,355,251×
13,229,497×
13,000,526×
11,771,300×
11,816,604×
12,616,519×
13,303,074×
12,736,908×
12,654,372×
12,161,511×
12,156,642×
11,871,594×
9,733,082×
11,828,855×
12,595,207×
11,718,660×
11,130,448×
12,632,655×
13,714,152×
13,811,871×
13,304,942×
12,538,738×
14,150,103×
16,809,860×
20,000,002×
17,841,588×
18,396,502×
20,813,159×
20,965,304×
18,993,782×
19,361,467×
18,417,375×
20,405,498×
19,376,594×
22,470,736×
22,607,330×
22,701,556×
24,092,265×
23,701,502×
25,701,509×
24,531,624×
25,090,122×
26,584,830×
26,021,508×
24,000,970×
20,616,697×
20,786,213×
19,985,920×
18,765,135×
20,139,336×
20,323,736×
20,184,142×
20,313,896×
20,940,966×
20,015,203×
20,258,470×
18,107,668×
18,631,714×
19,915,386×
20,364,016×
21,510,968×
23,544,541×
23,796,513×
23,799,877×
25,107,702×
27,304,787×
26,348,522×
24,525,162×
24,496,170×
26,463,883×
24,231,505×
22,749,982×
24,808,983×
23,473,909×
23,703,335×
25,411,132×
24,830,333×
22,047,376×
21,619,632×
21,989,222×
23,494,805×
21,338,206×
23,919,793×
23,482,072×
21,688,379×
22,223,301×
22,063,435×
21,136,696×
20,937,357×
23,017,367×
24,145,425×
26,002,965×
30,112,640×
29,912,736×
29,959,126×
29,465,688×
31,374,620×
30,274,053×
29,097,559×
29,736,609×
28,005,148×
28,200,629×
26,868,878×
25,298,818×
25,069,696×
26,377,844×
24,598,342×
25,342,908×
28,245,751×
34,698,529×
37,406,927×
35,385,471×
35,082,213×
36,522,409×
33,545,794×
34,888,927×
31,124,990×
30,689,454×
32,345,182×
30,116,221×
32,523,299×
34,407,811×
32,765,416×
31,600,993×
30,692,310×
28,095,739×
28,578,657×
28,564,130×
28,674,577×
28,392,748×
28,359,226×
26,572,595×
30,755,062×
34,144,015×
30,583,133×
25,754,933×
24,420,111×
23,702,949×
23,328,957×
25,166,278×
24,356,553×
23,513,003×
24,129,571×
22,807,704×
22,655,705×
23,855,938×
23,328,673×
23,706,203×
22,743,021×
23,878,500×
26,358,985×
24,588,085×
25,014,374×
24,285,717×
23,850,593×
22,160,318×
24,941,078×
24,679,962×
24,078,748×
23,258,478×
18,953,862×
17,913,844×
18,324,599×
16,691,806×
18,117,374×
19,698,521×
18,373,785×
17,059,990×
17,935,439×
19,582,345×
18,266,073×
17,790,590×
15,840,372×
14,037,578×
16,746,262×
15,289,380×
14,909,546×
15,525,268×
15,351,247×
14,189,748×
13,377,874×
13,085,766×
14,588,312×
16,584,371×
17,887,445×
18,597,524×
18,183,199×
18,435,214×
18,155,323×
17,697,975×
17,160,314×
19,246,768×
20,374,250×
18,119,342×
19,271,116×
19,881,819×
20,403,449×
22,211,109×
21,989,780×
21,831,792×
20,282,797×
19,418,297×
21,181,604×
20,558,503×
20,099,502×
17,317,364×
16,857,930×
17,048,344×
18,684,609×
17,426,519×
17,419,223×
19,439,594×
16,995,368×
17,569,467×
15,645,435×
16,172,164×
16,770,173×
15,551,442×
15,313,225×
14,904,480×
12,687,636×
12,859,383×
14,646,728×
12,795,837×
11,403,195×
12,099,810×
12,374,148×
10,901,737×
9,693,846×
9,923,021×
9,523,058×
9,382,574×
8,077,120×
6,714,859×
7,080,621×
8,398,163×
7,996,207×
8,058,210×
8,685,829×
8,648,478×
10,526,535×
10,516,397×
9,795,058×
10,687,058×
11,431,618×
11,878,214×
12,163,402×
11,764,238×
10,549,226×
11,450,657×
12,742,073×
14,338,596×
14,424,665×
14,172,968×
14,485,979×
13,833,808×
13,599,232×
15,302,108×
12,625,684×
12,942,272×
11,403,638×
11,606,697×
12,419,216×
10,517,893×
11,429,679×
10,427,430×
12,663,353×
14,102,522×
13,972,919×
14,505,598×
13,082,350×
13,093,694×
12,854,886×
11,806,548×
14,146,804×
14,822,755×
16,627,405×
15,283,490×
16,511,606×
14,757,492×
15,068,527×
17,391,584×
19,016,191×
17,306,024×
17,602,628×
16,620,219×
15,285,340×
12,218,559×
9,520,235×
9,932,147×
10,544,335×
10,598,686×
12,183,933×
10,869,344×
10,993,076×
9,667,198×
8,478,691×
8,997,216×
9,535,486×
9,085,750×
7,943,445×
7,160,338×
7,983,500×
6,554,745×
7,174,704×
7,614,164×
7,797,854×
8,114,345×
7,757,351×
7,250,828×
5,861,108×
5,874,672×
4,806,819×
6,136,405×
5,682,439×
5,909,582×
5,968,290×
6,316,988×
8,194,304×
8,243,024×
6,685,180×
5,501,320×
5,560,722×
4,855,790×
4,195,276×
4,688,580×
5,084,544×
4,943,100×
4,299,864×
3,229,618×
2,321,178×
2,817,397×
2,903,486×
2,945,309×
2,969,550×
1,982,022×
2,370,779×
2,322,294×
2,025,270×
2,285,130×
2,903,078×
2,732,701×
2,937,968×
1,812,660×
1,833,246×
2,159,520×
2,423,250×
2,032,676×
1,983,398×
1,787,186×
1,976,490×
2,810,901×
2,555,625×
2,503,628×
1,670,960×
1,564,590×
1,779,372×
2,666,600×
2,878,033×
3,221,634×
2,730,436×
3,109,628×
2,747,259×
2,299,524×
2,552,778×
2,348,848×
2,518,260×
2,085,332×
2,459,332×
2,027,507×
1,277,550×
1,211,710×
548,674×
360,752×
257,836×
678,800×
407,512×
291,512×
523,360×
429,668×
292,210×
299,254×
523,704×
259,656×
149,004×
422,382×
117,898×
99,936×
127,404×
200,076×
212,712×
184,860×
519,778×
805,058×
474,346×
625,848×
805,068×
1,185,718×
1,197,927×
818,973×
786,590×
880,246×
492,790×
812,610×
513,826×
732,944×
393,314×
585,828×
562,972×
828,884×
352,074×
622,716×
790,642×
749,740×
891,078×
757,024×
819,068×
1,280,614×
1,169,472×
577,272×
392,060×
486,718×
608,464×
345,654×
284,852×
344,034×
293,564×
469,022×
549,574×
315,684×
425,850×
317,014×
221,678×
143,644×
258,504×
302,664×
196,488×
140,218×
207,292×
141,212×
257,396×