Base 17: Iteration Frequencies: Full Cycle

Radix Character Encoding
0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V

Color Key
Orange	Fixed Point	number that becomes itself after one iteration
Green	Final Numbers	all numbers eventually reached, from all cycles
Purple	Cycle Start	iterations include entry into cycle, assuming it repeats
Red	Full Cycle	iterations include entire cycle, proving it repeats
Blue	Start Numbers	subset (optimization) of all numbers; minimal for full coverage
Gray	No Results	any calculation that has no results

Digits

Average Steps
Full Cycle

1.94 step
avg

4.31 step
avg

6.17 step
avg

5.68 step
avg

9.63 step
avg

16.49 step
avg

12.76 step
avg

16.27 step
avg

21.95 step
avg

41.88 step
avg

29.13 step
avg

45.47 step
avg

17.66 step
avg

47.26 step
avg

33.34 step
avg

31.65 step
avg

23.45 step
avg

96.63 step
avg

20.04 step
avg

55.57 step
avg

Step Frequency
Full Cycle

0s:
1s:
2s:
0×
1×
16×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
0×
2×
26×
14×
40×
23×
48×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
0×
1×
16×
161×
77×
152×
142×
128×
110×
88×
62×
32×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
0×
1×
16×
132×
368×
1,073×
2,596×
579×
80×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
13s:
14s:
15s:
0×
1×
16×
0×
0×
984×
1,550×
1,699×
3,487×
3,711×
2,148×
1,200×
1,281×
2,022×
1,634×
616×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
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30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
0×
1×
176×
769×
1,691×
1,329×
1,533×
3,740×
3,400×
5,283×
3,432×
3,622×
3,478×
1,951×
3,164×
3,569×
5,483×
3,331×
3,588×
3,250×
2,549×
2,155×
2,173×
2,491×
2,182×
749×
193×
416×
782×
1,153×
776×
349×
259×
351×
1,094×
659×
392×
505×
257×
414×
1,128×
796×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
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20s:
21s:
22s:
23s:
24s:
25s:
26s:
27s:
28s:
29s:
30s:
31s:
0×
1×
16×
2,168×
4,048×
8,411×
13,277×
18,338×
23,820×
28,270×
30,805×
18,819×
8,359×
5,821×
5,757×
10,067×
8,233×
6,881×
6,358×
5,232×
3,901×
3,064×
2,247×
2,212×
1,516×
3,599×
5,453×
8,125×
6,440×
3,425×
336×
158×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
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27s:
28s:
29s:
30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
0×
1×
16×
0×
952×
4,930×
24,393×
45,163×
51,561×
42,159×
35,158×
42,935×
27,839×
25,610×
18,626×
23,174×
33,307×
33,298×
26,092×
30,968×
36,500×
44,760×
19,875×
24,457×
39,992×
33,031×
13,848×
22,839×
15,928×
5,294×
6,085×
3,226×
1,386×
808×
353×
228×
272×
193×
124×
90×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
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35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
43s:
44s:
45s:
46s:
47s:
0×
1×
1,168×
2,673×
6,803×
5,600×
3,976×
8,851×
27,744×
47,707×
56,901×
74,258×
71,264×
90,639×
97,156×
97,229×
107,562×
106,274×
140,174×
107,711×
100,696×
63,103×
43,958×
52,253×
36,214×
26,657×
24,327×
33,547×
31,248×
54,807×
55,294×
58,347×
56,538×
46,196×
37,180×
25,178×
18,690×
26,752×
46,142×
39,349×
29,150×
17,290×
15,667×
14,765×
22,266×
9,849×
3,197×
624×

0s:
1s:
2s:
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44s:
45s:
46s:
47s:
48s:
49s:
50s:
51s:
52s:
53s:
54s:
55s:
0×
1×
16×
0×
0×
7,680×
32,676×
71,549×
84,750×
106,699×
110,848×
151,159×
265,511×
293,639×
220,330×
179,172×
216,184×
241,546×
255,692×
205,986×
265,201×
449,281×
359,917×
292,540×
265,735×
251,662×
302,315×
362,586×
437,490×
380,958×
442,592×
427,010×
523,613×
608,001×
788,362×
713,487×
591,003×
580,512×
527,950×
486,214×
391,782×
268,878×
191,437×
150,559×
173,536×
147,221×
71,021×
41,937×
14,836×
25,468×
18,012×
15,392×
10,516×
8,028×
7,580×
1,825×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
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68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
0×
1×
16×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
22,875×
176,593×
786,516×
1,297,925×
1,642,251×
2,010,500×
1,903,135×
2,152,168×
1,681,831×
1,446,607×
1,021,342×
1,722,524×
1,830,555×
1,224,953×
946,412×
838,150×
700,829×
650,675×
682,869×
650,915×
586,014×
331,676×
535,606×
413,024×
360,150×
225,965×
411,090×
294,297×
328,449×
885,315×
624,337×
635,139×
384,960×
299,245×
143,202×
105,738×
56,006×
102,925×
103,209×
127,298×
48,070×
21,395×
7,296×
112×
1,444×
39×
46×
66×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
8s:
9s:
10s:
11s:
12s:
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30s:
31s:
32s:
33s:
34s:
35s:
36s:
37s:
38s:
39s:
40s:
41s:
42s:
0×
1×
16×
0×
0×
12,672×
106,152×
465,724×
1,255,491×
1,563,779×
1,622,309×
2,683,163×
3,536,005×
4,567,617×
5,084,040×
5,410,804×
5,766,429×
5,004,981×
4,430,268×
3,569,773×
3,038,552×
3,478,386×
3,216,714×
3,029,212×
2,209,898×
1,884,228×
1,568,207×
1,157,916×
705,311×
490,289×
536,478×
428,154×
258,284×
155,913×
146,455×
132,030×
81,690×
68,488×
97,561×
82,305×
11,572×
6,544×
504×

0s:
1s:
2s:
3s:
4s:
5s:
6s:
7s:
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53s:
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56s:
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61s:
62s:
63s:
64s:
65s:
66s:
67s:
68s:
69s:
70s:
71s:
72s:
73s:
74s:
75s:
76s:
77s:
78s:
79s:
80s:
81s:
0×
1×
2,896×
25,212×
44,092×
4,640×
216×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
0×
35,315×
496,073×
3,129,823×
8,955,452×
8,620,864×
5,315,103×
7,262,554×
7,770,863×
7,575,919×
6,931,647×
6,059,704×
4,106,301×
4,435,238×
4,505,356×
5,166,202×
4,518,594×
5,200,500×
4,148,990×
4,723,864×
6,953,200×
3,956,666×
4,115,724×
4,029,033×
3,386,195×
3,817,928×
2,541,182×
1,873,545×
2,676,350×
2,973,608×
1,837,589×
1,446,668×
1,029,318×
577,514×
992,864×
774,826×
494,977×
255,244×
238,056×
242,016×
602,425×
397,031×
211,848×
270,479×
428,206×
154,588×
60,361×
45,025×
3,914×
876×

0s:
1s:
2s:
3s:
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52s:
53s:
54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
0×
1×
11,032×
146,988×
545,364×
965,105×
937,509×
1,734,521×
1,760,226×
1,388,012×
1,525,103×
2,174,354×
2,386,898×
3,159,033×
3,905,646×
3,794,334×
3,390,028×
3,598,769×
4,063,847×
3,837,820×
4,150,023×
5,042,918×
4,289,442×
4,514,087×
5,717,530×
5,960,163×
7,037,883×
8,468,693×
8,993,743×
9,395,628×
9,570,167×
10,855,450×
9,896,418×
9,742,396×
10,461,330×
10,973,003×
11,890,307×
12,327,566×
13,265,369×
12,036,894×
10,827,959×
9,302,051×
7,530,328×
6,994,156×
6,458,953×
4,708,957×
4,617,967×
4,635,995×
3,886,112×
3,144,505×
3,069,121×
3,581,744×
3,301,181×
2,726,484×
2,490,537×
2,348,185×
2,620,499×
1,587,606×
967,664×
769,785×
660,605×
264,853×
93,446×
33,350×
4,552×

0s:
1s:
2s:
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54s:
55s:
56s:
57s:
58s:
59s:
60s:
61s:
62s:
63s:
64s:
65s:
66s:
0×
1×
16×
0×
0×
0×
5,839×
118,724×
599,071×
1,902,639×
1,943,277×
979,436×
3,375,673×
13,853,996×
12,472,140×
9,567,456×
5,911,580×
7,123,566×
4,527,296×
6,501,533×
11,642,014×
10,179,199×
15,620,947×
16,627,106×
15,526,474×
27,680,946×
24,214,204×
23,965,459×
28,323,976×
24,461,526×
27,227,156×
28,514,577×
23,094,296×
26,094,186×
18,327,924×
17,368,219×
17,678,117×
16,751,737×
10,000,680×
10,133,829×
9,941,052×
11,780,782×
12,101,201×
13,461,161×
8,884,635×
7,021,727×
11,515,520×
15,974,289×
12,732,296×
6,677,795×
5,309,075×
5,572,116×
4,110,973×
2,496,604×
1,195,898×
1,511,979×
2,044,180×
1,868,316×
1,156,650×
851,215×
982,775×
183,968×
141,506×
294,711×
866,703×
88,354×
94×

0s:
1s:
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61s:
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66s:
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68s:
69s:
0×
1×
16×
19,584×
452,240×
1,410,472×
1,648,008×
3,616,772×
5,297,060×
8,951,910×
22,751,459×
32,585,474×
38,567,633×
51,775,101×
55,769,010×
50,010,091×
48,718,947×
48,382,235×
44,814,206×
36,338,727×
34,341,512×
34,961,647×
42,191,943×
47,784,135×
55,058,215×
44,101,737×
45,737,159×
47,963,846×
45,844,941×
35,083,357×
40,997,168×
38,700,842×
40,745,977×
32,499,343×
24,100,043×
15,112,516×
11,295,216×
7,281,325×
5,953,951×
3,683,766×
3,250,767×
3,899,835×
4,528,688×
4,868,366×
5,095,012×
3,890,720×
4,727,700×
3,030,247×
2,885,500×
3,203,723×
4,306,406×
4,476,797×
1,761,710×
1,400,461×
1,990,760×
1,718,968×
1,160,484×
1,461,446×
969,085×
891,248×
560,784×
650,516×
383,764×
178,164×
193,220×
413,588×
239,788×
89,400×
27,808×
570×

0s:
1s:
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0×
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1,168×
14,384×
101,768×
293,345×
57,538×
140,988×
2,202,112×
10,857,785×
8,474,334×
1,849,661×
1,363,802×
2,326,958×
2,309,453×
2,096,647×
88,997×
499,499×
39,806×
19,507×
467,550×
129,425×
87,064×
137,592×
3,888×
2,732×
0×
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154,749×
4,147,046×
32,162,669×
102,328,199×
124,858,247×
97,038,887×
81,494,809×
75,549,063×
63,796,885×
79,565,113×
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94,675,752×
80,541,893×
48,478,004×
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69,545,050×
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22,509,991×
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8,284,071×
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3,919,304×
1,780,068×
1,163,846×
2,154,750×
1,002,366×
80,947×
37,043×
69,293×
208×
150×
58×

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0×
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16×
44,064×
1,162,368×
4,948,529×
11,597,328×
25,968,499×
57,580,761×
85,215,177×
132,790,590×
140,243,372×
178,001,257×
185,417,520×
207,532,161×
202,566,061×
204,483,124×
241,547,374×
253,901,933×
238,964,825×
201,609,303×
211,713,371×
190,679,548×
162,046,097×
136,010,837×
131,396,796×
118,688,828×
100,861,437×
102,192,281×
87,693,337×
63,612,976×
39,634,087×
30,026,334×
21,807,960×
22,373,049×
33,546,886×
49,965,639×
41,091,843×
35,052,975×
30,857,842×
23,808,871×
19,627,787×
14,961,303×
7,598,451×
4,855,537×
2,685,621×
2,045,238×
1,011,010×
403,029×
103,677×
2,040×

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0×
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16×
0×
9,189×
495,687×
4,444,568×
19,132,749×
22,330,878×
16,613,983×
5,723,660×
2,987,531×
347,998×
682,778×
377,020×
39,766×
12,144×
0×
59,999×
2,660,452×
25,995,816×
106,407,856×
85,237,546×
128,556,204×
165,885,260×
143,114,826×
139,107,925×
100,786,654×
88,840,145×
166,836,919×
95,685,519×
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10,052,497×
22,423,232×
48,577,804×
66,435,499×
94,957,487×
239,430,943×
232,577,246×
143,081,465×
111,360,869×
88,300,794×
140,137,298×
222,169,305×
196,449,280×
178,773,898×
138,707,755×
177,220,835×
101,076,963×
102,773,930×
89,000,151×
134,177,257×
147,782,033×
142,414,485×
98,025,080×
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90,467,938×
107,984,589×
50,771,537×
67,188,722×
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36,296,932×
68,168,930×
90,032,658×
51,403,499×
41,682,953×
37,019,915×
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42,113,122×
32,509,752×
14,588,615×
46,240,014×
57,040,656×
56,566,304×
86,626,650×
90,496,099×
72,226,194×
110,397,772×
95,842,726×
66,711,786×
64,455,825×
40,035,803×
35,015,377×
30,655,511×
14,598,530×
11,192,286×
29,006,988×
30,902,285×
19,013,814×
30,538,690×
28,963,371×
19,222,039×
27,208,868×
110,291,202×
54,050,205×
29,001,362×
21,914,336×
35,972,786×
39,138,063×
47,062,359×
12,031,391×
9,423,449×
9,673,626×
7,516,930×
6,148,461×
1,764,597×
2,133,247×
2,263,357×
178,137×
102,286×
2,376×
1,704×