Base 169: Iteration Frequencies: Cycle Start

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
W	X	Y	Z	a	b	c	d	e	f	g	h	i	j	k	l
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ

Radix Character Encoding

ァ

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

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	1	2	3	4	5
Average Steps Cycle Start	0.99 step avg	2.23 step avg	32.85 step avg	1.77 step avg	33.13 step avg
Step Frequency Cycle Start	0s: 1s: 1× 168×	0s: 1s: 2s: 3s: 22× 3,717× 3,570× 7,056×	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: 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: 1× 14,617× 7,221× 14,440× 14,430× 14,416× 14,398× 14,376× 14,350× 14,320× 14,286× 14,248× 14,206× 14,160× 14,110× 14,056× 13,998× 13,936× 13,870× 13,800× 13,726× 13,648× 13,566× 13,480× 13,390× 13,296× 13,198× 13,096× 12,990× 12,880× 12,766× 12,648× 12,526× 12,400× 12,270× 12,136× 11,998× 11,856× 11,710× 11,560× 11,406× 11,248× 11,086× 10,920× 10,750× 10,576× 10,398× 10,216× 10,030× 9,840× 9,646× 9,448× 9,246× 9,040× 8,830× 8,616× 8,398× 8,176× 7,950× 7,720× 7,486× 7,248× 7,006× 6,760× 6,510× 6,256× 5,998× 5,736× 5,470× 5,200× 4,926× 4,648× 4,366× 4,080× 3,790× 3,496× 3,198× 2,896× 2,590× 2,280× 1,966× 1,648× 1,326× 1,000× 670× 336×	0s: 1s: 2s: 3s: 4s: 1× 8,691,928× 25,888,450× 621,012× 7,224×	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: 1× 1,295,330× 1,010,337× 1,032,499× 2,235,364× 2,962,973× 4,196,225× 4,778,785× 6,817,133× 6,771,768× 8,673,015× 8,900,187× 10,803,378× 11,635,280× 12,994,221× 14,472,625× 15,222,464× 17,380,882× 17,465,483× 20,329,479× 19,701,110× 23,288,612× 21,907,633× 27,231,366× 24,619,993× 31,935,939× 27,736,964× 37,025,715× 32,083,742× 40,321,820× 35,576,525× 42,138,677× 38,171,447× 42,882,868× 37,567,030× 40,285,773× 36,239,709× 37,857,955× 34,358,390× 36,842,726× 31,414,227× 36,397,458× 28,722,102× 33,540,147× 26,342,176× 29,434,584× 24,880,265× 25,554,206× 21,480,045× 22,148,439× 18,038,025× 18,021,525× 14,589,426× 13,385,407× 10,119,979× 8,877,433× 6,354,304× 4,647,640× 3,268,355× 2,131,908× 1,214,045× 610,131× 250,877× 43,952×

Digits

Average Steps
Cycle Start

0.99 step
avg

2.23 step
avg

32.85 step
avg

1.77 step
avg

33.13 step
avg

Step Frequency
Cycle Start

0s:
1s:
1×
168×

0s:
1s:
2s:
3s:
22×
3,717×
3,570×
7,056×

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:
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:
1×
14,617×
7,221×
14,440×
14,430×
14,416×
14,398×
14,376×
14,350×
14,320×
14,286×
14,248×
14,206×
14,160×
14,110×
14,056×
13,998×
13,936×
13,870×
13,800×
13,726×
13,648×
13,566×
13,480×
13,390×
13,296×
13,198×
13,096×
12,990×
12,880×
12,766×
12,648×
12,526×
12,400×
12,270×
12,136×
11,998×
11,856×
11,710×
11,560×
11,406×
11,248×
11,086×
10,920×
10,750×
10,576×
10,398×
10,216×
10,030×
9,840×
9,646×
9,448×
9,246×
9,040×
8,830×
8,616×
8,398×
8,176×
7,950×
7,720×
7,486×
7,248×
7,006×
6,760×
6,510×
6,256×
5,998×
5,736×
5,470×
5,200×
4,926×
4,648×
4,366×
4,080×
3,790×
3,496×
3,198×
2,896×
2,590×
2,280×
1,966×
1,648×
1,326×
1,000×
670×
336×

0s:
1s:
2s:
3s:
4s:
1×
8,691,928×
25,888,450×
621,012×
7,224×

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:
1×
1,295,330×
1,010,337×
1,032,499×
2,235,364×
2,962,973×
4,196,225×
4,778,785×
6,817,133×
6,771,768×
8,673,015×
8,900,187×
10,803,378×
11,635,280×
12,994,221×
14,472,625×
15,222,464×
17,380,882×
17,465,483×
20,329,479×
19,701,110×
23,288,612×
21,907,633×
27,231,366×
24,619,993×
31,935,939×
27,736,964×
37,025,715×
32,083,742×
40,321,820×
35,576,525×
42,138,677×
38,171,447×
42,882,868×
37,567,030×
40,285,773×
36,239,709×
37,857,955×
34,358,390×
36,842,726×
31,414,227×
36,397,458×
28,722,102×
33,540,147×
26,342,176×
29,434,584×
24,880,265×
25,554,206×
21,480,045×
22,148,439×
18,038,025×
18,021,525×
14,589,426×
13,385,407×
10,119,979×
8,877,433×
6,354,304×
4,647,640×
3,268,355×
2,131,908×
1,214,045×
610,131×
250,877×
43,952×

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
W	X	Y	Z	a	b	c	d	e	f	g	h	i	j	k	l
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ

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
W	X	Y	Z	a	b	c	d	e	f	g	h	i	j	k	l
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ

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
W	X	Y	Z	a	b	c	d	e	f	g	h	i	j	k	l
m	n	o	p	q	r	s	t	u	v	w	x	y	z	Α	Β
Γ	Δ	Ε	Ζ	Η	Θ	Ι	Κ	Λ	Μ	Ν	Ξ	Ο	Π	Ρ	Σ
Τ	Υ	Φ	Χ	Ψ	Ω	α	β	γ	δ	ε	ζ	η	θ	ι	κ
λ	μ	ν	ξ	ο	π	ρ	ς	σ	τ	υ	φ	χ	ψ	ω	А
Б	В	Г	Д	Е	Ж	З	И	Й	К	Л	М	Н	О	П	Р
С	Т	У	Ф	Х	Ц	Ч	Ш	Щ	Ъ	Ы	Ь	Э	Ю	Я	а
б	в	г	д	е	ж	з	и	й	к	л	м	н	о	п	р
с	т	у	ф	х	ц	ч	ш	щ	ъ	ы	ь	э	ю	я	ァ