Count up with recursive prime factorization

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tomtom2357
Posts: 563
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Re: Count up with recursive prime factorization

Postby tomtom2357 » Tue Feb 02, 2016 11:21 am UTC

611
<<><<>>><<<>><<<>>>>
<ab><bc>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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emlightened
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Re: Count up with recursive prime factorization

Postby emlightened » Tue Feb 02, 2016 11:24 am UTC

612
<><><<>><<>><<<><>>>
ab<<aa>>ba
Image

@faubi: That looks fine.
Bleb. Idk when I'm returning.

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Tue Feb 02, 2016 9:01 pm UTC

613
<<><><><><<><>>>
<aaaa<aa>>
p<p1p1p1p1p<p1p1>>
211111112113

Code: Select all

***********
* * * * ***
        * *
Image

Prime: Yes
Symmetrical: Yes
Alphabetical: No

Length: 16
Reversals: 11
Max Depth: 3
Factors: 1
Smoothness: 613
Necessary Brackets: 4

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emlightened
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Re: Count up with recursive prime factorization

Postby emlightened » Thu Feb 04, 2016 8:26 am UTC

614
<><<<>><<>><<><>>>
a<bb<aa>>
Image
Bleb. Idk when I'm returning.

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Thu Feb 04, 2016 10:42 am UTC

615
<<>><<<>>><<<><<>>>>
bc<<ab>>
pp1ppp1p<p<p1pp1>>
22333124

Code: Select all

* * ***
* * ***
  * * *
      *
Image

Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 7
Max Depth: 4
Factors: 3
Smoothness: 41
Necessary Brackets: 4

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emlightened
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Re: Count up with recursive prime factorization

Postby emlightened » Thu Feb 04, 2016 11:40 am UTC

616
<><><><<><>><<<<>>>>
aaa<aa>d
Image
Bleb. Idk when I'm returning.

tomtom2357
Posts: 563
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Re: Count up with recursive prime factorization

Postby tomtom2357 » Thu Feb 04, 2016 11:41 am UTC

617
<<<><<>><<<>>>>>
<<abc>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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emlightened
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Re: Count up with recursive prime factorization

Postby emlightened » Thu Feb 04, 2016 11:48 am UTC

618
<><<>><<<>><<>><<>>>
ab<bbb>
Image
Bleb. Idk when I'm returning.

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Thu Feb 04, 2016 12:36 pm UTC

619
<<><<>><<><><>>>
<ab<aaa>>
p<p1pp1p<p1p1p1>>
2122211113

Code: Select all

*********
* * *****
  * * * *
Image

Prime: Yes
Symmetrical: No
Alphabetical: No

Length: 16
Reversals: 9
Max Depth: 3
Factors: 1
Smoothness: 619
Necessary Brackets: 4

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

Re: Count up with recursive prime factorization

Postby tomtom2357 » Fri Feb 05, 2016 3:54 am UTC

620
<><><<<>>><<<<<>>>>>
aace
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Fri Feb 05, 2016 4:09 am UTC

621
<<>><<>><<>><<<>><<>>>
bbb<bb>
pp1pp1pp1p<pp1pp1>
2222223223

Code: Select all

* * * ***
* * * * *
      * *
Image

Prime: No
Symmetrical: No
Alphabetical: No

Length: 22
Reversals: 9
Max Depth: 3
Factors: 4
Smoothness: 23
Necessary Brackets: 2

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

Re: Count up with recursive prime factorization

Postby tomtom2357 » Fri Feb 05, 2016 9:35 am UTC

<><<><><><><><>>
a<aaaaaa>
P(w6+1)
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Fri Feb 05, 2016 6:55 pm UTC

623
<<><>><<><><><<>>>
<aa><aaab>
p<p1p1>p<p1p1p1pp1>
211221111123

Code: Select all

*** *******
* * * * * *
          *
Image

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 11
Max Depth: 3
Factors: 2
Smoothness: 89
Necessary Brackets: 4

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emlightened
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Re: Count up with recursive prime factorization

Postby emlightened » Fri Feb 05, 2016 8:31 pm UTC

624
<><><><><<>><<><<>>>
aaaab<ab>
Image
Bleb. Idk when I'm returning.

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Sat Feb 06, 2016 1:26 am UTC

625
<<<>>><<<>>><<<>>><<<>>>
cccc
ppp1ppp1ppp1ppp1
33333333

Code: Select all

* * * *
* * * *
* * * *
Image

Prime: No
Symmetrical: Yes
Alphabetical: Yes

Length: 24
Reversals: 7
Max Depth: 3
Factors: 4
Smoothness: 5
Necessary Brackets: 0

Another integer power.

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emlightened
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Re: Count up with recursive prime factorization

Postby emlightened » Sun Feb 07, 2016 10:22 pm UTC

626
<><<><><><<><<>>>>
a<c<ab>>
Image
Bleb. Idk when I'm returning.

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Mon Feb 08, 2016 7:59 am UTC

627
<<>><<<<>>>><<><><>>
bd<aaa>
pp1pppp1p<p1p1p1>
2244211112

Code: Select all

* * *****
* * * * *
  *     
  *     
Image

Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 9
Max Depth: 4
Factors: 3
Smoothness: 19
Necessary Brackets: 2

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

Re: Count up with recursive prime factorization

Postby Elmach » Wed Jul 20, 2016 12:49 am UTC

The number is 628.

Here's a new notation!
103242301
423230101

In the more standard bracket-notation,
<><<<><<>><>>><>
<<<<>><><>>><><>
1131221311 look and see notation
4211131111 also look and see notation
symmetric, not alphabetic, composite
Half-length: 7
Reversals: 9
Depth: 4
Image
in pink ordinals (fora, echo), whatever they are.

628l.png
628l.png (421 Bytes) Viewed 1668 times

(note: boundary notation, not level-set. 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.

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Fri Jul 22, 2016 3:14 pm UTC

629
<<<><>>><<><><<>>>
65.9% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Tue Jul 26, 2016 3:37 pm UTC

630
<><<>><<>><<<>>><<><>>
abbc<aa>
p1pp1pp1ppp1p<p1p1>
112222332112

Code: Select all

* * * * ***
  * * * * *
      *   
Image

Prime: No
Symmetrical: No
Alphabetical: No

Length: 22
Reversals: 11
Max Depth: 3
Factors: 5
Smoothness: 7
Necessary Brackets: 2

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Tue Jul 26, 2016 4:21 pm UTC

631
<<<<>>><<<>><<>>>>
65.92% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

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ygh
Posts: 4
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Re: Count up with recursive prime factorization

Postby ygh » Thu Jul 28, 2016 5:48 pm UTC

632
<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".

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faubiguy
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Re: Count up with recursive prime factorization

Postby faubiguy » Thu Jul 28, 2016 10:40 pm UTC

633
<<>><<<<>><<<>>>>>
b<<bc>>
pp1p<p<pp1ppp1>>
224235

Code: Select all

* ***
* ***
  * *
  * *
    *
Image

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 211
Necessary Brackets: 4

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Fri Jul 29, 2016 10:43 pm UTC

634
<><<><<>><<<<>>>>>
65.95% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

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ygh
Posts: 4
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Re: Count up with recursive prime factorization

Postby ygh » Sat Jul 30, 2016 3:14 am UTC

635
cf
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Sat Jul 30, 2016 10:20 pm UTC

636
<><><<>><<><><><>>
65.96% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

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ygh
Posts: 4
Joined: Fri Jun 17, 2016 7:22 pm UTC

Re: Count up with recursive prime factorization

Postby ygh » Sun Jul 31, 2016 12:06 am UTC

637-
<aa><aa><ab>
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Mon Aug 01, 2016 8:41 am UTC

638
<><<<<>>>><<><<<>>>>
64.35% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

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ygh
Posts: 4
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Re: Count up with recursive prime factorization

Postby ygh » Sat Aug 06, 2016 11:43 pm UTC

639

<<>><<><><<<>>>><<>>
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Sun Aug 07, 2016 3:32 pm UTC

640
<><><><><><><><<<>>>
64.36% efficiency.
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

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ygh
Posts: 4
Joined: Fri Jun 17, 2016 7:22 pm UTC

Re: Count up with recursive prime factorization

Postby ygh » Sun Aug 07, 2016 7:22 pm UTC

641
<aa<ac>>
I don't know what I'm doing most of the time.
Example: I often hit "quote" instead of "edit".

User avatar
phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Tue Aug 09, 2016 2:53 pm UTC

642
<><<>><<><><<><>>>
66.01% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

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Sabrar
Posts: 37
Joined: Tue Nov 03, 2015 6:29 pm UTC

Re: Count up with recursive prime factorization

Postby Sabrar » Tue Aug 09, 2016 3:12 pm UTC

643
<<<>><<>><<><<>>>>

Elmach
Posts: 155
Joined: Sun Mar 13, 2011 7:47 am UTC

Re: Count up with recursive prime factorization

Postby Elmach » Fri Aug 12, 2016 5:49 am UTC

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;
ωω2 + ω2 + 2

I'm wondering, how many people are using a program, and how many are doing this manually?

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faubiguy
Posts: 15
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Re: Count up with recursive prime factorization

Postby faubiguy » Fri Aug 12, 2016 1:11 pm UTC

645
<<>><<<>>><<><<><>>>
bc<a<aa>>
pp1ppp1p<p1p<p1p1>>
2233212113

Code: Select all

* * *****
* * * ***
  *   * *
Image

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

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Sabrar
Posts: 37
Joined: Tue Nov 03, 2015 6:29 pm UTC

Re: Count up with recursive prime factorization

Postby Sabrar » Fri Aug 12, 2016 3:35 pm UTC

646
<><<<><>>><<><><>>

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Sat Aug 13, 2016 1:13 am UTC

647
<<><<<<><>>>>>
69.94% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

User avatar
Sabrar
Posts: 37
Joined: Tue Nov 03, 2015 6:29 pm UTC

Re: Count up with recursive prime factorization

Postby Sabrar » Sat Aug 13, 2016 4:07 am UTC

648
<><><><<>><<>><<>><<>>

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phillip1882
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Re: Count up with recursive prime factorization

Postby phillip1882 » Sat Aug 13, 2016 9:36 pm UTC

649
<<<<>>>><<<<><>>>>
66.07% efficiency
bitcoin address: 18vbN38FT7XXhazcN8gWichBwzC47MHy5p

User avatar
Sabrar
Posts: 37
Joined: Tue Nov 03, 2015 6:29 pm UTC

Re: Count up with recursive prime factorization

Postby Sabrar » Mon Aug 15, 2016 8:14 am UTC

650
<><<<>>><<<>>><<><<>>>


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