Count up with recursive prime factorization
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 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
611
<<><<>>><<<>><<<>>>>
<ab><bc>
<<><<>>><<<>><<<>>>>
<ab><bc>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
 emlightened
 Posts: 36
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
612
<><><<>><<>><<<><>>>
ab<<aa>>ba
@faubi: That looks fine.
<><><<>><<>><<<><>>>
ab<<aa>>ba
@faubi: That looks fine.
Bleb. Idk when I'm returning.
Re: Count up with recursive prime factorization
613
<<><><><><<><>>>
<aaaa<aa>>
p<p1p1p1p1p<p1p1>>
211111112113
Prime: Yes
Symmetrical: Yes
Alphabetical: No
Length: 16
Reversals: 11
Max Depth: 3
Factors: 1
Smoothness: 613
Necessary Brackets: 4
<<><><><><<><>>>
<aaaa<aa>>
p<p1p1p1p1p<p1p1>>
211111112113
Code: Select all
***********
* * * * ***
* *
Prime: Yes
Symmetrical: Yes
Alphabetical: No
Length: 16
Reversals: 11
Max Depth: 3
Factors: 1
Smoothness: 613
Necessary Brackets: 4
 emlightened
 Posts: 36
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
614
<><<<>><<>><<><>>>
a<bb<aa>>
<><<<>><<>><<><>>>
a<bb<aa>>
Bleb. Idk when I'm returning.
Re: Count up with recursive prime factorization
615
<<>><<<>>><<<><<>>>>
bc<<ab>>
pp1ppp1p<p<p1pp1>>
22333124
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 7
Max Depth: 4
Factors: 3
Smoothness: 41
Necessary Brackets: 4
<<>><<<>>><<<><<>>>>
bc<<ab>>
pp1ppp1p<p<p1pp1>>
22333124
Code: Select all
* * ***
* * ***
* * *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 7
Max Depth: 4
Factors: 3
Smoothness: 41
Necessary Brackets: 4
 emlightened
 Posts: 36
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
616
<><><><<><>><<<<>>>>
aaa<aa>d
<><><><<><>><<<<>>>>
aaa<aa>d
Bleb. Idk when I'm returning.

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
617
<<<><<>><<<>>>>>
<<abc>>
<<<><<>><<<>>>>>
<<abc>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
 emlightened
 Posts: 36
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
618
<><<>><<<>><<>><<>>>
ab<bbb>
<><<>><<<>><<>><<>>>
ab<bbb>
Bleb. Idk when I'm returning.
Re: Count up with recursive prime factorization
619
<<><<>><<><><>>>
<ab<aaa>>
p<p1pp1p<p1p1p1>>
2122211113
Prime: Yes
Symmetrical: No
Alphabetical: No
Length: 16
Reversals: 9
Max Depth: 3
Factors: 1
Smoothness: 619
Necessary Brackets: 4
<<><<>><<><><>>>
<ab<aaa>>
p<p1pp1p<p1p1p1>>
2122211113
Code: Select all
*********
* * *****
* * * *
Prime: Yes
Symmetrical: No
Alphabetical: No
Length: 16
Reversals: 9
Max Depth: 3
Factors: 1
Smoothness: 619
Necessary Brackets: 4

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
620
<><><<<>>><<<<<>>>>>
aace
<><><<<>>><<<<<>>>>>
aace
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
621
<<>><<>><<>><<<>><<>>>
bbb<bb>
pp1pp1pp1p<pp1pp1>
2222223223
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 9
Max Depth: 3
Factors: 4
Smoothness: 23
Necessary Brackets: 2
<<>><<>><<>><<<>><<>>>
bbb<bb>
pp1pp1pp1p<pp1pp1>
2222223223
Code: Select all
* * * ***
* * * * *
* *
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 9
Max Depth: 3
Factors: 4
Smoothness: 23
Necessary Brackets: 2

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
<><<><><><><><>>
a<aaaaaa>
P(w^{6}+1)
a<aaaaaa>
P(w^{6}+1)
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
623
<<><>><<><><><<>>>
<aa><aaab>
p<p1p1>p<p1p1p1pp1>
211221111123
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 11
Max Depth: 3
Factors: 2
Smoothness: 89
Necessary Brackets: 4
<<><>><<><><><<>>>
<aa><aaab>
p<p1p1>p<p1p1p1pp1>
211221111123
Code: Select all
*** *******
* * * * * *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 11
Max Depth: 3
Factors: 2
Smoothness: 89
Necessary Brackets: 4
 emlightened
 Posts: 36
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
624
<><><><><<>><<><<>>>
aaaab<ab>
<><><><><<>><<><<>>>
aaaab<ab>
Bleb. Idk when I'm returning.
Re: Count up with recursive prime factorization
625
<<<>>><<<>>><<<>>><<<>>>
cccc
ppp1ppp1ppp1ppp1
33333333
Prime: No
Symmetrical: Yes
Alphabetical: Yes
Length: 24
Reversals: 7
Max Depth: 3
Factors: 4
Smoothness: 5
Necessary Brackets: 0
Another integer power.
<<<>>><<<>>><<<>>><<<>>>
cccc
ppp1ppp1ppp1ppp1
33333333
Code: Select all
* * * *
* * * *
* * * *
Prime: No
Symmetrical: Yes
Alphabetical: Yes
Length: 24
Reversals: 7
Max Depth: 3
Factors: 4
Smoothness: 5
Necessary Brackets: 0
Another integer power.
 emlightened
 Posts: 36
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
626
<><<><><><<><<>>>>
a<c<ab>>
<><<><><><<><<>>>>
a<c<ab>>
Bleb. Idk when I'm returning.
Re: Count up with recursive prime factorization
627
<<>><<<<>>>><<><><>>
bd<aaa>
pp1pppp1p<p1p1p1>
2244211112
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 9
Max Depth: 4
Factors: 3
Smoothness: 19
Necessary Brackets: 2
<<>><<<<>>>><<><><>>
bd<aaa>
pp1pppp1p<p1p1p1>
2244211112
Code: Select all
* * *****
* * * * *
*
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 9
Max Depth: 4
Factors: 3
Smoothness: 19
Necessary Brackets: 2
Re: Count up with recursive prime factorization
The number is 628.
Here's a new notation!
103242301
423230101
In the more standard bracketnotation,
<><<<><<>><>>><>
<<<<>><><>>><><>
1131221311 look and see notation
4211131111 also look and see notation
symmetric, not alphabetic, composite
Halflength: 7
Reversals: 9
Depth: 4
in pink ordinals (fora, echo), whatever they are.
(note: boundary notation, not levelset. The boundary between blobs represents the rooted tree formation thing.)
Minimal square is 11*11 or 9*9, depending on counting method.
Minimal area is 9*13 or 7*11. First number is twice depth ± 1. Obvious proof. Twice depth ± 1 is the smallest number.
Here's a new notation!
103242301
423230101
In the more standard bracketnotation,
<><<<><<>><>>><>
<<<<>><><>>><><>
1131221311 look and see notation
4211131111 also look and see notation
symmetric, not alphabetic, composite
Halflength: 7
Reversals: 9
Depth: 4
in pink ordinals (fora, echo), whatever they are.
(note: boundary notation, not levelset. The boundary between blobs represents the rooted tree formation thing.)
Minimal square is 11*11 or 9*9, depending on counting method.
Minimal area is 9*13 or 7*11. First number is twice depth ± 1. Obvious proof. Twice depth ± 1 is the smallest number.
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
629
<<<><>>><<><><<>>>
65.9% efficiency
<<<><>>><<><><<>>>
65.9% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
630
<><<>><<>><<<>>><<><>>
abbc<aa>
p1pp1pp1ppp1p<p1p1>
112222332112
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 11
Max Depth: 3
Factors: 5
Smoothness: 7
Necessary Brackets: 2
<><<>><<>><<<>>><<><>>
abbc<aa>
p1pp1pp1ppp1p<p1p1>
112222332112
Code: Select all
* * * * ***
* * * * *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 11
Max Depth: 3
Factors: 5
Smoothness: 7
Necessary Brackets: 2
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
631
<<<<>>><<<>><<>>>>
65.92% efficiency
<<<<>>><<<>><<>>>>
65.92% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
632
<ad>aaa
<ad>aaa
Last edited by ygh on Sat Jul 30, 2016 3:15 am UTC, edited 1 time in total.
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".
Example: I often hit "quote" instead of "edit".
Re: Count up with recursive prime factorization
633
<<>><<<<>><<<>>>>>
b<<bc>>
pp1p<p<pp1ppp1>>
224235
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 211
Necessary Brackets: 4
<<>><<<<>><<<>>>>>
b<<bc>>
pp1p<p<pp1ppp1>>
224235
Code: Select all
* ***
* ***
* *
* *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 211
Necessary Brackets: 4
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
634
<><<><<>><<<<>>>>>
65.95% efficiency
<><<><<>><<<<>>>>>
65.95% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
635
cf
cf
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".
Example: I often hit "quote" instead of "edit".
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
636
<><><<>><<><><><>>
65.96% efficiency
<><><<>><<><><><>>
65.96% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
637
<aa><aa><ab>
<aa><aa><ab>
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".
Example: I often hit "quote" instead of "edit".
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
638
<><<<<>>>><<><<<>>>>
64.35% efficiency
<><<<<>>>><<><<<>>>>
64.35% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
639
<<>><<><><<<>>>><<>>
<<>><<><><<<>>>><<>>
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".
Example: I often hit "quote" instead of "edit".
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
640
<><><><><><><><<<>>>
64.36% efficiency.
<><><><><><><><<<>>>
64.36% efficiency.
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
641
<aa<ac>>
<aa<ac>>
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".
Example: I often hit "quote" instead of "edit".
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
642
<><<>><<><><<><>>>
66.01% efficiency
<><<>><<><><<><>>>
66.01% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
643
<<<>><<>><<><<>>>>
<<<>><<>><<><<>>>>
Re: Count up with recursive prime factorization
AarexTiaokhiao wrote:<<><>>
<<<>><<>>>
161
Times four makes my number, 644. Thus, we have
<><><<><>><<<>><<>>>
Code: Select all
*** *** * *
* * * *
* *
I like this notation; it's easy to read.
That's four factors.
You can count the nodes at each level;
4, 4, 2, 0, 0...
This gives max depth and factors automatically.
The length is twice the sum: 10 ↦ 20.
Since the depth is less than five, you can use bbcode for the ordinal number;
ω^{ω2} + ω^{2} + 2
I'm wondering, how many people are using a program, and how many are doing this manually?
Re: Count up with recursive prime factorization
645
<<>><<<>>><<><<><>>>
bc<a<aa>>
pp1ppp1p<p1p<p1p1>>
2233212113
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 9
Max Depth: 3
Factors: 3
Smoothness: 43
Necessary Brackets: 4
I've been using a program for a while now. Here's the current version
<<>><<<>>><<><<><>>>
bc<a<aa>>
pp1ppp1p<p1p<p1p1>>
2233212113
Code: Select all
* * *****
* * * ***
* * *
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 9
Max Depth: 3
Factors: 3
Smoothness: 43
Necessary Brackets: 4
I've been using a program for a while now. Here's the current version
Re: Count up with recursive prime factorization
646
<><<<><>>><<><><>>
<><<<><>>><<><><>>
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
647
<<><<<<><>>>>>
69.94% efficiency
<<><<<<><>>>>>
69.94% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
648
<><><><<>><<>><<>><<>>
<><><><<>><<>><<>><<>>
 phillip1882
 Posts: 95
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
649
<<<<>>>><<<<><>>>>
66.07% efficiency
<<<<>>>><<<<><>>>>
66.07% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p
Re: Count up with recursive prime factorization
650
<><<<>>><<<>>><<><<>>>
<><<<>>><<<>>><<><<>>>
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