Date: 4/05/2021 02:04:01
From: dv
ID: 1733331
Subject: Distinct patterns
0







null
1






O
R1
2





O
per R1
3





O O
R3
4




O

per R1
5




O
O
R5
6




O O
per R3
7




O O O
R7
8



O


per R1
9



O

O
R9
10



O
O
per R5
11



O
O O
R11
12



O O

per R3
13



O O
O
R13
14



O O O
per R7
15



O O O O
R15
16


O



per R1
17


O


O per R1
18


O

O
per R9
19


O

O O
R19
20


O
O

per R5
21


O
O
O
R21
22


O
O O
per R11
23


O
O O O
R23
24


O O


per R3
25


O O

O
R25
26


O O
O
per R13
27


O O
O O
R27
28


O O O

per R7
29


O O O
O
R29
30


O O O O
per R15
31


O O O O O
R31
32

O




per R1
33

O



O per R9
34

O


O
per R1
35

O


O O per R25
36

O

O

per R9
37

O

O
O
R37
38

O

O O
per R19
39

O

O O O
R39
40

O
O


per R5
41

O
O

O per R37
42

O
O
O
per R21
43

O
O
O O
R43
44

O
O O

per R11
45

O
O O
O
R45
46

O
O O O
per R23
47

O
O O O O
R47
48

O O



per R3
49

O O


O per R19
50

O O

O
per R25
51

O O

O O per R5
52

O O
O

per R13
53

O O
O
O
R53
54

O O
O O
per R27
55

O O
O O O
R55
56

O O O


per R7
57

O O O

O per R39
58

O O O
O
per R29
59

O O O
O O
R59
60

O O O O

per R15
61

O O O O
O
R61
62

O O O O O
per R31
63

O O O O O O
R63
64
O





per R1
65
O




O per R5
66
O



O
per R9
67
O



O O per R13
68
O


O

per R1
69
O


O
O per R21
70
O


O O
per R25
71
O


O O O per R29
72
O

O


per R9
73
O

O

O per R37
74
O

O
O
per R37
75
O

O
O O per R45
76
O

O O

per R19
77
O

O O
O per R53
78
O

O O O
per R39
79
O

O O O O per R61
80
O
O



per R5
81
O
O


O per R21
82
O
O

O
per R37
83
O
O

O O per R53
84
O
O
O

per R21
85
O
O
O
O per R1
86
O
O
O O
per R43
87
O
O
O O O
R87
88
O
O O


per R11
89
O
O O

O per R43
90
O
O O
O
per R45
91
O
O O
O O
R91
92
O
O O O

per R23
93
O
O O O
O per R87
94
O
O O O O
per R47
95
O
O O O O O
R95
96
O O




per R3
97
O O



O per R11
98
O O


O
per R19
99
O O


O O per R27
100
O O

O

per R25
101
O O

O
O per R43
102
O O

O O
per R5
103
O O

O O O per R59
104
O O
O


per R13
105
O O
O

O per R45
106
O O
O
O
per R53
107
O O
O
O O per R91
108
O O
O O

per R27
109
O O
O O
O per R91
110
O O
O O O
per R55
111
O O
O O O O
R111
112
O O O



per R7
113
O O O


O per R23
114
O O O

O
per R39
115
O O O

O O per R55
116
O O O
O

per R29
117
O O O
O
O per R87
118
O O O
O O
per R59
119
O O O
O O O per R21
120
O O O O


per R15
121
O O O O

O per R47
122
O O O O
O
per R61
123
O O O O
O O per R111
124
O O O O O

per R31
125
O O O O O
O per R95
126
O O O O O O
per R63
127
O O O O O O O
R127
128 O






per R1
129 O





O per R3
130 O




O
per R5
131 O




O O per R7
132 O



O

per R9
133 O



O
O per R11
134 O



O O
per R13
135 O



O O O per R15
136 O


O


per R1
137 O


O

O per R19
138 O


O
O
per R21
139 O


O
O O per R23
140 O


O O

per R25
141 O


O O
O per R27
142 O


O O O
per R29
143 O


O O O O per R31
144 O

O



per R9
145 O

O


O per R25
146 O

O

O
per R37
147 O

O

O O per R39
148 O

O
O

per R37
149 O

O
O
O per R43
150 O

O
O O
per R45
151 O

O
O O O per R47
152 O

O O


per R19
153 O

O O

O per R5
154 O

O O
O
per R53
155 O

O O
O O per R55
156 O

O O O

per R39
157 O

O O O
O per R59
158 O

O O O O
per R61
159 O

O O O O O per R63
160 O
O




per R5
161 O
O



O per R13
162 O
O


O
per R21
163 O
O


O O per R29
164 O
O

O

per R37
165 O
O

O
O per R45
166 O
O

O O
per R53
167 O
O

O O O per R61
168 O
O
O


per R21
169 O
O
O

O per R53
170 O
O
O
O
per R1
171 O
O
O
O O per R87
172 O
O
O O

per R43
173 O
O
O O
O per R107
174 O
O
O O O
per R87
175 O
O
O O O O per R95
176 O
O O



per R11
177 O
O O


O per R27
178 O
O O

O
per R43
179 O
O O

O O per R59
180 O
O O
O

per R45
181 O
O O
O
O per R91
182 O
O O
O O
per R91
183 O
O O
O O O per R111
184 O
O O O


per R23
185 O
O O O

O per R55
186 O
O O O
O
per R87
187 O
O O O
O O per R21
188 O
O O O O

per R47
189 O
O O O O
O per R111
190 O
O O O O O
per R95
191 O
O O O O O O per R127
192 O O





per R3
193 O O




O per R7
194 O O



O
per R11
195 O O



O O per R15
196 O O


O

per R19
197 O O


O
O per R23
198 O O


O O
per R27
199 O O


O O O per R31
200 O O

O


per R25
201 O O

O

O per R39
202 O O

O
O
per R43
203 O O

O
O O per R47
204 O O

O O

per R5
205 O O

O O
O per R55
206 O O

O O O
per R59
207 O O

O O O O per R63
208 O O
O



per R13
209 O O
O


O per R29
210 O O
O

O
per R45
211 O O
O

O O per R61
212 O O
O
O

per R53
213 O O
O
O
O per R87
214 O O
O
O O
per R91
215 O O
O
O O O per R95
216 O O
O O


per R27
217 O O
O O

O per R59
218 O O
O O
O
per R91
219 O O
O O
O O per R111
220 O O
O O O

per R55
221 O O
O O O
O per R21
222 O O
O O O O
per R111
223 O O
O O O O O per R127
224 O O O




per R7
225 O O O



O per R15
226 O O O


O
per R23
227 O O O


O O per R31
228 O O O

O

per R39
229 O O O

O
O per R47
230 O O O

O O
per R55
231 O O O

O O O per R63
232 O O O
O


per R29
233 O O O
O

O per R61
234 O O O
O
O
per R87
235 O O O
O
O O per R95
236 O O O
O O

per R59
237 O O O
O O
O per R111
238 O O O
O O O
per R21
239 O O O
O O O O per R127
240 O O O O



per R15
241 O O O O


O per R31
242 O O O O

O
per R47
243 O O O O

O O per R63
244 O O O O
O

per R61
245 O O O O
O
O per R95
246 O O O O
O O
per R111
247 O O O O
O O O per R127
248 O O O O O


per R31
249 O O O O O

O per R63
250 O O O O O
O
per R95
251 O O O O O
O O per R127
252 O O O O O O

per R63
253 O O O O O O
O per R127
254 O O O O O O O
per R127
255 O O O O O O O O per R1

Check my working, SCIENCE, but I think there are 30 distinct patterns.

Reply Quote
Date: 4/05/2021 03:47:21
From: mollwollfumble
ID: 1733333
Subject: re: Distinct patterns

Distinct patterns? I think I missed something.

2^8 = 256 as you have.
8*9/2 = 36 permutations

Reply Quote
Date: 4/05/2021 09:01:07
From: The Rev Dodgson
ID: 1733343
Subject: re: Distinct patterns

Last row is “perR1”?

How does that work?

Reply Quote
Date: 4/05/2021 09:21:55
From: The Rev Dodgson
ID: 1733345
Subject: re: Distinct patterns

I think we need a definition of what constitutes a “pattern”.

Reply Quote
Date: 4/05/2021 20:34:30
From: SCIENCE
ID: 1733611
Subject: re: Distinct patterns

The Rev Dodgson said:

mollwollfumble said:
dv said:
Check my working, SCIENCE,

8*9/2 = 36 permutations

Last row is “perR1”? How does that work?

I think we need a definition of what constitutes a “pattern”.

Good evening all, we’ve just had a think over dinner but concede that we have no immediate / obvious / cheap / dirty hack of a solution unlike the thermodynamic trick we played on Divine Angel’s Digest where the number of possible ways to divide 4 optionsets according to 3 options was 6! / 4!2!.

We’ll set out our thoughts in following responses but this first is to specifically address the above.

Without explicitly specifying a compressed pattern description then it’s difficult to judge whether a given sequence fits the pattern (as others have also alluded to there are up to 256 possibilities) but we are presuming that the intended description is something like “sequences of 8 bits that are unique up to rotational symmetry” so until otherwise advised that’s what we’ll be working off.

—

mollwollfumble offers 9! / 7!2! without qualification so we’ren’t sure of its basis but invite further explanation.

—

The Rev Dodgson seems to agree with us that {255 O O O O O O O O per R1} seems erroneous conferatur {17 _ _ _ O _ _ _ O per R1} but that is on the basis of the pattern we have presumed.

If any of you have alternative descriptors please advise.

Reply Quote
Date: 4/05/2021 21:47:48
From: sibeen
ID: 1733630
Subject: re: Distinct patterns

Could someone give me some background out of where this discussion come from?

Reply Quote
Date: 5/05/2021 00:40:11
From: SCIENCE
ID: 1733704
Subject: re: Distinct patterns

Anyway having dug around for a bit and coded some entertainment we conclude that:

Reply Quote
Date: 5/05/2021 01:09:46
From: dv
ID: 1733707
Subject: re: Distinct patterns

Well I’ve had my fun and I hope you did too. How many unique patterns could be created by placing markers on a field of eight successive locations if we consider that there’s no particular starting location (effectively they are looped, such that the 7th is followed by the 0th, and if we consider that the lateral scale is irrelevant.

Consider it as a musical beat, looped. A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

A beat in which there are two intervals of the same length followed by an interval of double that length is represented by 21, 42, 69, 81, 84, 119, 138, 162, 168, 187, 221, 238.

Reply Quote
Date: 5/05/2021 07:54:15
From: The Rev Dodgson
ID: 1733750
Subject: re: Distinct patterns

dv said:


Well I’ve had my fun and I hope you did too. How many unique patterns could be created by placing markers on a field of eight successive locations if we consider that there’s no particular starting location (effectively they are looped, such that the 7th is followed by the 0th, and if we consider that the lateral scale is irrelevant.

Consider it as a musical beat, looped. A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

A beat in which there are two intervals of the same length followed by an interval of double that length is represented by 21, 42, 69, 81, 84, 119, 138, 162, 168, 187, 221, 238.

My mystification increases. In SCIENCE’s first link:
“a(1) = 2 = #{ “0”, “1” },

a(2) = 1 = #{ “01” },

a(3) = 2 = #{ “001”, “011” },”

if a(1) is allowed “0” and “1”, why isn’t a(2) allowed “00” or “11”, and so on?

Reply Quote
Date: 5/05/2021 08:41:23
From: SCIENCE
ID: 1733761
Subject: re: Distinct patterns

The Rev Dodgson said:


dv said:

Well I’ve had my fun and I hope you did too. How many unique patterns could be created by placing markers on a field of eight successive locations if we consider that there’s no particular starting location (effectively they are looped, such that the 7th is followed by the 0th, and if we consider that the lateral scale is irrelevant.

Consider it as a musical beat, looped. A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

A beat in which there are two intervals of the same length followed by an interval of double that length is represented by 21, 42, 69, 81, 84, 119, 138, 162, 168, 187, 221, 238.

My mystification increases. In SCIENCE’s first link:
“a(1) = 2 = #{ “0”, “1” },

a(2) = 1 = #{ “01” },

a(3) = 2 = #{ “001”, “011” },”

if a(1) is allowed “0” and “1”, why isn’t a(2) allowed “00” or “11”, and so on?

what if we draw your attention to the context of that first link,

with primitive period n” where the length (n) is 8, videre licet https://oeis.org/A001037

and similarly dv’s concept of uniqueness or degeneracy

A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

especially say 1 versus 17 versus 85 versus 255 which respectively hexadecimalise to 1,11,55,FF id est regular patterns as claimed

Reply Quote
Date: 5/05/2021 09:45:18
From: The Rev Dodgson
ID: 1733783
Subject: re: Distinct patterns

SCIENCE said:


The Rev Dodgson said:

dv said:

Well I’ve had my fun and I hope you did too. How many unique patterns could be created by placing markers on a field of eight successive locations if we consider that there’s no particular starting location (effectively they are looped, such that the 7th is followed by the 0th, and if we consider that the lateral scale is irrelevant.

Consider it as a musical beat, looped. A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

A beat in which there are two intervals of the same length followed by an interval of double that length is represented by 21, 42, 69, 81, 84, 119, 138, 162, 168, 187, 221, 238.

My mystification increases. In SCIENCE’s first link:
“a(1) = 2 = #{ “0”, “1” },

a(2) = 1 = #{ “01” },

a(3) = 2 = #{ “001”, “011” },”

if a(1) is allowed “0” and “1”, why isn’t a(2) allowed “00” or “11”, and so on?

what if we draw your attention to the context of that first link,

with primitive period n” where the length (n) is 8, videre licet https://oeis.org/A001037

and similarly dv’s concept of uniqueness or degeneracy

A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

especially say 1 versus 17 versus 85 versus 255 which respectively hexadecimalise to 1,11,55,FF id est regular patterns as claimed

In that case why isn’t 119 per1, rather than per21?

Reply Quote
Date: 5/05/2021 09:57:00
From: SCIENCE
ID: 1733787
Subject: re: Distinct patterns

The Rev Dodgson said:

why isn’t 119 per1, rather than per21?

the fellow posts many things and we don’t understand all of them

when we find our higher-bandwidth-mind-machine-interface electronic computer we’ll give you our code if we have time

Reply Quote
Date: 5/05/2021 10:10:31
From: The Rev Dodgson
ID: 1733795
Subject: re: Distinct patterns

SCIENCE said:


The Rev Dodgson said:
why isn’t 119 per1, rather than per21?

the fellow posts many things and we don’t understand all of them

when we find our higher-bandwidth-mind-machine-interface electronic computer we’ll give you our code if we have time

OK, thanks for your assistance.

I will wait to see if the fellow responds himself.

Reply Quote
Date: 5/05/2021 10:20:35
From: dv
ID: 1733808
Subject: re: Distinct patterns

The Rev Dodgson said:


dv said:

Well I’ve had my fun and I hope you did too. How many unique patterns could be created by placing markers on a field of eight successive locations if we consider that there’s no particular starting location (effectively they are looped, such that the 7th is followed by the 0th, and if we consider that the lateral scale is irrelevant.

Consider it as a musical beat, looped. A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

A beat in which there are two intervals of the same length followed by an interval of double that length is represented by 21, 42, 69, 81, 84, 119, 138, 162, 168, 187, 221, 238.

My mystification increases. In SCIENCE’s first link:
“a(1) = 2 = #{ “0”, “1” },

a(2) = 1 = #{ “01” },

a(3) = 2 = #{ “001”, “011” },”

if a(1) is allowed “0” and “1”, why isn’t a(2) allowed “00” or “11”, and so on?

I’m afraid I don’t understand this.

There’s a reason I left the blank fields blank.

Reply Quote
Date: 5/05/2021 10:28:43
From: dv
ID: 1733816
Subject: re: Distinct patterns

The Rev Dodgson said:


SCIENCE said:

The Rev Dodgson said:

My mystification increases. In SCIENCE’s first link:
“a(1) = 2 = #{ “0”, “1” },

a(2) = 1 = #{ “01” },

a(3) = 2 = #{ “001”, “011” },”

if a(1) is allowed “0” and “1”, why isn’t a(2) allowed “00” or “11”, and so on?

what if we draw your attention to the context of that first link,

with primitive period n” where the length (n) is 8, videre licet https://oeis.org/A001037

and similarly dv’s concept of uniqueness or degeneracy

A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

especially say 1 versus 17 versus 85 versus 255 which respectively hexadecimalise to 1,11,55,FF id est regular patterns as claimed

In that case why isn’t 119 per1, rather than per21?

Per1 is a regular beat. Or to put it another, a constant interval between hits.

Per21 has two intervals of a given length, followed by an interval double that length.

Reply Quote
Date: 5/05/2021 10:33:43
From: SCIENCE
ID: 1733820
Subject: re: Distinct patterns

it’d be interesting to see how dv coded the algorithm to assign all these, seems a bit of hard work

Reply Quote
Date: 5/05/2021 10:36:46
From: The Rev Dodgson
ID: 1733823
Subject: re: Distinct patterns

dv said:


The Rev Dodgson said:

SCIENCE said:

what if we draw your attention to the context of that first link,

with primitive period n” where the length (n) is 8, videre licet https://oeis.org/A001037

and similarly dv’s concept of uniqueness or degeneracy

A simple regular drum beat is represented by any of the options 1, 2, 4, 8, 16, 17, 32, 34, 64, 68, 85, 128, 136, 170, 255.

especially say 1 versus 17 versus 85 versus 255 which respectively hexadecimalise to 1,11,55,FF id est regular patterns as claimed

In that case why isn’t 119 per1, rather than per21?

Per1 is a regular beat. Or to put it another, a constant interval between hits.

Per21 has two intervals of a given length, followed by an interval double that length.

That’s why I think 119 should be as 1, not 21, since 119 has a constant interval of 1.

Reply Quote
Date: 5/05/2021 10:37:42
From: dv
ID: 1733824
Subject: re: Distinct patterns

The Rev Dodgson said:


dv said:

The Rev Dodgson said:

In that case why isn’t 119 per1, rather than per21?

Per1 is a regular beat. Or to put it another, a constant interval between hits.

Per21 has two intervals of a given length, followed by an interval double that length.

That’s why I think 119 should be as 1, not 21, since 119 has a constant interval of 1.

The circles represent hits, not misses

Reply Quote
Date: 5/05/2021 10:38:26
From: SCIENCE
ID: 1733827
Subject: re: Distinct patterns

The Rev Dodgson said:

I think 119 should be as 1, not 21, since 119 has a constant interval of 1.

doesn’t it have ._o_o_o._o_o_o which is not a constant interval between o

Reply Quote
Date: 5/05/2021 10:38:43
From: The Rev Dodgson
ID: 1733828
Subject: re: Distinct patterns

SCIENCE said:


it’d be interesting to see how dv coded the algorithm to assign all these, seems a bit of hard work

I’m tempted to have a go in Excel, but fortunately I’m busy so I won’t.

Reply Quote
Date: 5/05/2021 10:41:34
From: The Rev Dodgson
ID: 1733831
Subject: re: Distinct patterns

dv said:


The Rev Dodgson said:

dv said:

Per1 is a regular beat. Or to put it another, a constant interval between hits.

Per21 has two intervals of a given length, followed by an interval double that length.

That’s why I think 119 should be as 1, not 21, since 119 has a constant interval of 1.

The circles represent hits, not misses

That’s what I was assuming.

Reply Quote
Date: 5/05/2021 10:43:55
From: The Rev Dodgson
ID: 1733832
Subject: re: Distinct patterns

SCIENCE said:


The Rev Dodgson said:
I think 119 should be as 1, not 21, since 119 has a constant interval of 1.

doesn’t it have ._o_o_o._o_o_o which is not a constant interval between o

It looked to me like: -000-000, which is a constant interval between groups of 0s

Reply Quote
Date: 5/05/2021 10:46:46
From: SCIENCE
ID: 1733833
Subject: re: Distinct patterns

The Rev Dodgson said:


SCIENCE said:

The Rev Dodgson said:
I think 119 should be as 1, not 21, since 119 has a constant interval of 1.

doesn’t it have ._o_o_o._o_o_o which is not a constant interval between o

It looked to me like: -000-000, which is a constant interval between groups of 0s

yeah we think dv meant the intervals here are 2,1,1,2,1,1 and for say R21 they are 4,2,2 which is equivalent stretched

and probably also enjoyed the confusion

Reply Quote
Date: 5/05/2021 10:58:43
From: dv
ID: 1733837
Subject: re: Distinct patterns

The Rev Dodgson said:


SCIENCE said:

The Rev Dodgson said:
I think 119 should be as 1, not 21, since 119 has a constant interval of 1.

doesn’t it have ._o_o_o._o_o_o which is not a constant interval between o

It looked to me like: -000-000, which is a constant interval between groups of 0s

Each of 0 is a hit. Nul hit hit hit nul hit hit hit

Reply Quote
Date: 5/05/2021 11:00:53
From: dv
ID: 1733839
Subject: re: Distinct patterns

SCIENCE said:


The Rev Dodgson said:

SCIENCE said:

doesn’t it have ._o_o_o._o_o_o which is not a constant interval between o

It looked to me like: -000-000, which is a constant interval between groups of 0s

yeah we think dv meant the intervals here are 2,1,1,2,1,1 and for say R21 they are 4,2,2 which is equivalent stretched

and probably also enjoyed the confusion

I nerdsniped myself into this and there’s no reason you should not suffer

Reply Quote
Date: 5/05/2021 11:04:19
From: SCIENCE
ID: 1733843
Subject: re: Distinct patterns

fortunately, in our code, the difference between the 2 similar definitions is a single conditional

Reply Quote
Date: 5/05/2021 11:32:11
From: The Rev Dodgson
ID: 1733857
Subject: re: Distinct patterns

From my e-mail:

Quora “suggested spaces”
Space Cover Photo

Math Worksheets · 13.1k followers
Post your best Math Worksheets… the more you practice, the better you get!
The next number in the series 1, 1, 2, 3, 5, 8, 13, 21 is?

A coincidence?

I think not.

Reply Quote
Date: 5/05/2021 11:59:23
From: SCIENCE
ID: 1733880
Subject: re: Distinct patterns

Probably takes more effort to sneak this past the Textile processing than to invent in the first place, but hoping it makes it, here you go.

—

<!DOCTYPE HTML><html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Sequence</title></head>
<body><pre id="output"></pre>
<script type="application/javascript" ><!--
"use strict";
(function () {

 var d;        // number of binary digits
 var bs = [];  // unique or referral identifiers for binary sequences
 var b, s;     // shifted sequence, shift offset
 var n, nn;    // counter, duplicated counter

   // because we use a shift and mask hack in this algorithm, we restrict computation to 8 bits
 for (d = 0; d < 8; ) { d++;

    // this part initialises the array of sequence
  for (n = 0; n < Math.pow(2, d); n++) {
   bs[n] = 0;
  }

  for (n = 0; n < Math.pow(2, d); n++) {
   nn = n | (n << d);                       // duplicate the counter to enable shift and mask
   if (bs[n] == 0) {                        // only process new unique sequences
    bs[n] = -1;                             //   mark sequence as unique
    for (s = 1; s < d; s++) {               //   rotate through shifted sequences
     b = (nn >> s) & (Math.pow(2, d) - 1);  //     shift and mask
     if (b != n) {                          // *** this is the conditional that determines which definition applies; when removed the algorithm will mark patterns with shorter primitive periods as referring to themselves (rather than -1 unique)
      bs[b] = n;                            //       mark rotationally identical sequences as referring to the earliest unique match
     }
    }
   }
  }

    // count the number of unique sequences and make output
  b = 0;
  for (n = 0; n < Math.pow(2, d); n++) {
   document.getElementById("output").insertAdjacentText("beforeend", ("0".repeat(3) + n.toString(10)).substr(-3) + "  " + ("0".repeat(d) + n.toString(2)).substr(-d) + "  " + bs[n] + "\n");
   if (bs[n] < 0) {
    b++;
   }
  }
  document.getElementById("output").insertAdjacentText("beforeend", "\nBits: " + d.toString(10) + " | Uniques: " + b.toString(10) + "\n\n---\n\n");

 }

})();
//--></script>
</body></html>

Reply Quote
Date: 5/05/2021 12:07:01
From: Michael V
ID: 1733886
Subject: re: Distinct patterns

The Rev Dodgson said:


From my e-mail:

Quora “suggested spaces”
Space Cover Photo

Math Worksheets · 13.1k followers
Post your best Math Worksheets… the more you practice, the better you get!
The next number in the series 1, 1, 2, 3, 5, 8, 13, 21 is?

A coincidence?

I think not.

34

Reply Quote
Date: 5/05/2021 12:17:34
From: The Rev Dodgson
ID: 1733891
Subject: re: Distinct patterns

Michael V said:


The Rev Dodgson said:

From my e-mail:

Quora “suggested spaces”
Space Cover Photo

Math Worksheets · 13.1k followers
Post your best Math Worksheets… the more you practice, the better you get!
The next number in the series 1, 1, 2, 3, 5, 8, 13, 21 is?

A coincidence?

I think not.

34

At last.

Something I can agree with in this thread.

Reply Quote
Date: 5/05/2021 12:20:23
From: Michael V
ID: 1733894
Subject: re: Distinct patterns

The Rev Dodgson said:


Michael V said:

The Rev Dodgson said:

From my e-mail:

Quora “suggested spaces”
Space Cover Photo

Math Worksheets · 13.1k followers
Post your best Math Worksheets… the more you practice, the better you get!
The next number in the series 1, 1, 2, 3, 5, 8, 13, 21 is?

A coincidence?

I think not.

34

At last.

Something I can agree with in this thread.

:)

Reply Quote
Date: 5/05/2021 12:23:19
From: sibeen
ID: 1733898
Subject: re: Distinct patterns

The Rev Dodgson said:


Michael V said:

The Rev Dodgson said:

From my e-mail:

Quora “suggested spaces”
Space Cover Photo

Math Worksheets · 13.1k followers
Post your best Math Worksheets… the more you practice, the better you get!
The next number in the series 1, 1, 2, 3, 5, 8, 13, 21 is?

A coincidence?

I think not.

34

At last.

Something I can agree with in this thread.

I think you’re all Fibbing.

Reply Quote
Date: 5/05/2021 12:24:56
From: The Rev Dodgson
ID: 1733899
Subject: re: Distinct patterns

sibeen said:


The Rev Dodgson said:

Michael V said:

34

At last.

Something I can agree with in this thread.

I think you’re all Fibbing.

What does the Federation International du Beton have to do with it?

Reply Quote
Date: 5/05/2021 12:26:13
From: SCIENCE
ID: 1733900
Subject: re: Distinct patterns

The Rev Dodgson said:


Michael V said:

The Rev Dodgson said:

From my e-mail:

Quora “suggested spaces”
Space Cover Photo

Math Worksheets · 13.1k followers
Post your best Math Worksheets… the more you practice, the better you get!
The next number in the series 1, 1, 2, 3, 5, 8, 13, 21 is?

A coincidence?

I think not.

34

At last.

Something I can agree with in this thread.

(from The Penguin Dictionary of Curious and Interesting Numbers)

it is quite the shortest entry for any natural number in the book up to that point, but they do not count it as uninteresting instead reserving that for a few pages later

Reply Quote
Date: 5/05/2021 12:29:50
From: The Rev Dodgson
ID: 1733901
Subject: re: Distinct patterns

SCIENCE said:


The Rev Dodgson said:

Michael V said:

34

At last.

Something I can agree with in this thread.

(from The Penguin Dictionary of Curious and Interesting Numbers)

it is quite the shortest entry for any natural number in the book up to that point, but they do not count it as uninteresting instead reserving that for a few pages later


I’m not sure I approve of their resolution of the “lowest uninteresting number” problem.

Reply Quote
Date: 5/05/2021 12:31:24
From: SCIENCE
ID: 1733903
Subject: re: Distinct patterns

SCIENCE said:


The Rev Dodgson said:

Michael V said:

34

At last.

Something I can agree with in this thread.

(from The Penguin Dictionary of Curious and Interesting Numbers)

it is quite the shortest entry for any natural number in the book up to that point, but they do not count it as uninteresting instead reserving that for a few pages later


and since any of you didn’t ask we looked up magic hexagons just for fun

Although there are no normal magical hexagons with order greater than 3, certain abnormal ones do exist. In this case, abnormal means starting the sequence of numbers other than with 1. Arsen Zahray discovered these order 4 and 5 hexagons:

…

https://en.wikipedia.org/wiki/Magic_hexagon

Reply Quote
Date: 5/05/2021 12:32:18
From: SCIENCE
ID: 1733905
Subject: re: Distinct patterns

The Rev Dodgson said:


SCIENCE said:

The Rev Dodgson said:

At last.

Something I can agree with in this thread.

(from The Penguin Dictionary of Curious and Interesting Numbers)

it is quite the shortest entry for any natural number in the book up to that point, but they do not count it as uninteresting instead reserving that for a few pages later


I’m not sure I approve of their resolution of the “lowest uninteresting number” problem.

the author is a David, not a Douglas, if that matters

Reply Quote
Date: 5/05/2021 12:40:39
From: The Rev Dodgson
ID: 1733908
Subject: re: Distinct patterns

SCIENCE said:


The Rev Dodgson said:

SCIENCE said:

(from The Penguin Dictionary of Curious and Interesting Numbers)

it is quite the shortest entry for any natural number in the book up to that point, but they do not count it as uninteresting instead reserving that for a few pages later


I’m not sure I approve of their resolution of the “lowest uninteresting number” problem.

the author is a David, not a Douglas, if that matters

Probably explains it :)

Reply Quote
Date: 6/05/2021 00:39:36
From: dv
ID: 1734167
Subject: re: Distinct patterns

I made a mistake anyway. 173 should say per91.

Reply Quote
Date: 6/05/2021 00:44:46
From: dv
ID: 1734168
Subject: re: Distinct patterns

R5 and R21 have 12 members, R1 has 15 members, and the remaining groups all have 8 members.

Reply Quote
Date: 6/05/2021 00:46:43
From: sibeen
ID: 1734169
Subject: re: Distinct patterns

dv said:


I made a mistake anyway. 173 should say per91.

I fucken knew it!

Reply Quote
Date: 6/05/2021 01:09:16
From: dv
ID: 1734172
Subject: re: Distinct patterns

If you do a scatter plot of “member” versus “all members that are equivalent to member including self” it looks like this.

Reply Quote
Date: 6/05/2021 09:33:08
From: The Rev Dodgson
ID: 1734225
Subject: re: Distinct patterns

dv said:


If you do a scatter plot of “member” versus “all members that are equivalent to member including self” it looks like this.


Very pretty.

So what software are you using for doing all this?

Reply Quote
Date: 6/05/2021 09:35:10
From: The Rev Dodgson
ID: 1734226
Subject: re: Distinct patterns

sibeen said:


dv said:

I made a mistake anyway. 173 should say per91.

I fucken knew it!

We’re all agreed then.

(They don’t look the same to me, but I’ll say nothing).

Reply Quote
Date: 6/05/2021 09:37:08
From: dv
ID: 1734227
Subject: re: Distinct patterns

The Rev Dodgson said:


dv said:

If you do a scatter plot of “member” versus “all members that are equivalent to member including self” it looks like this.


Very pretty.

So what software are you using for doing all this?

Coded in python but displayed that graph in excel

Reply Quote
Date: 6/05/2021 09:44:32
From: The Rev Dodgson
ID: 1734228
Subject: re: Distinct patterns

dv said:


The Rev Dodgson said:

dv said:

If you do a scatter plot of “member” versus “all members that are equivalent to member including self” it looks like this.


Very pretty.

So what software are you using for doing all this?

Coded in python but displayed that graph in excel

The code would be interesting, should you wish to share.

Reply Quote
Date: 6/05/2021 14:05:01
From: dv
ID: 1734397
Subject: re: Distinct patterns

If you allow only 1 slot there is only 1 pattern, obv. Same with 2m when you got to 3 slots there are 2 possible patterns.

1 1
2 1
3 2
4 3
5 6
6 9
7 18
8 30

Reply Quote
Date: 6/05/2021 18:57:43
From: dv
ID: 1734631
Subject: re: Distinct patterns

dv said:


If you allow only 1 slot there is only 1 pattern, obv. Same with 2m when you got to 3 slots there are 2 possible patterns.

1 1
2 1
3 2
4 3
5 6
6 9
7 18
8 30

And 9 has 56 … shrug emoji

Reply Quote