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.

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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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

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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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

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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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

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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faubiguy
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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

"Therefore it is in the interests not only of public safety but also public sanity if the buttered toast on cats idea is scrapped, to be replaced by a monorail powered by cats smeared with chicken tikka masala floating above a rail made from white shag pile carpet."

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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 2083 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
good luck have fun

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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
good luck have fun

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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 » 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.

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faubiguy
Posts: 15
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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
good luck have fun

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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 » Sat Jul 30, 2016 3:14 am UTC

635
cf
I don't know what I'm doing.

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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
good luck have fun

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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.

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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
good luck have fun

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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 » Sat Aug 06, 2016 11:43 pm UTC

639

<<>><<><><<<>>>><<>>
I don't know what I'm doing.

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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.
good luck have fun

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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.

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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
good luck have fun

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Sabrar
Posts: 42
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: 42
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
good luck have fun

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Sabrar
Posts: 42
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
good luck have fun

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Sabrar
Posts: 42
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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