Count up with recursive prime factorization

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Sat Apr 01, 2017 7:35 pm UTC

691
<<<<>>><<<>>><<<>>>>
<ccc>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

User avatar
phillip1882
Posts: 111
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
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Re: Count up with recursive prime factorization

Postby phillip1882 » Sun Apr 02, 2017 1:41 am UTC

692
<><><<><><><<<>>>>
72.66% efficiency
good luck have fun

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Sun Apr 02, 2017 2:00 am UTC

693
<<>><<>><<><>><<<<>>>>
bb<aa>d
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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phillip1882
Posts: 111
Joined: Fri Jun 14, 2013 9:11 pm UTC
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Re: Count up with recursive prime factorization

Postby phillip1882 » Sun Apr 02, 2017 10:20 pm UTC

694
<><<<>><<<>><<>>>>
72.69% efficiency
good luck have fun

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

Re: Count up with recursive prime factorization

Postby Elmach » Mon Apr 03, 2017 2:15 am UTC

695
<<<>>><<><<<><>>>>
c<a<<aa>>>
Fp(Pd(PP))
33213114

Code: Select all

* *****
* * ***
*   ***
    * *

Image
tertius et prīmus (prīmī et secundī bisprīmī)
695bl.png
7 by 5 with four extra dots; not happy with how the image turned out at the bottom right of the 139.
695bl.png (3.47 KiB) Viewed 2071 times

Spoiler:
695bl2.png
A little happier with this version,
695bl2.png (3.44 KiB) Viewed 2069 times

695bl3.png
or maybe this one.
695bl3.png (3.45 KiB) Viewed 2066 times

695b5al.png
A version with arms
695b5al.png (1.56 KiB) Viewed 2063 times

Semiprime
Asymmetric
Not Alphabetic
square-free, but recursively only cube-free

Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 139

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Mon Apr 03, 2017 10:17 am UTC

696
<><><><<>><<><<<>>>>
aaab<ac>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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

Re: Count up with recursive prime factorization

Postby Elmach » Tue Apr 04, 2017 1:05 am UTC

697
<<<><>>><<<><<>>>>
<<aa>><<ab>>
d(PP)d(PD)
31133124

Code: Select all

*** ***
*** ***
* * * *
      *

Image
secundus bisprīmī et secundus (prīmī et secundī)

697al.png
8 by 4 with one dot extra
697al.png (1.43 KiB) Viewed 2050 times

Semiprime
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 41

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Tue Apr 04, 2017 1:24 am UTC

698
<><<>><<<<>><<>>>>
ab<<bb>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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

Re: Count up with recursive prime factorization

Postby Elmach » Tue Apr 04, 2017 1:55 am UTC

699
<<>><<<>><<<><>>>>
b<b<<aa>>>
Dp(Dd(PP))
22323114

Code: Select all

* *****
* * ***
  * ***
    * *

Image
secundus et prīmus (secundī et secundī bisprīmī)
699l.png
6 by 5 exactly.
699l.png (1.59 KiB) Viewed 2039 times

Semiprime
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 7
Max Depth: 4
Smoothness: 233

----
Mistaken labyrinth notation, where I replaced a 3 with a 5, making 1165.
Spoiler:
699l.png
7 by 6 with seven unused dots, not optimal - EDIT: WRONG - this is 1165.
699l.png (1.67 KiB) Viewed 2048 times

User avatar
phillip1882
Posts: 111
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Re: Count up with recursive prime factorization

Postby phillip1882 » Wed Apr 05, 2017 11:36 pm UTC

700
<><><<<>>><<<>>><<><>>
59.56% efficiency
good luck have fun

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

Re: Count up with recursive prime factorization

Postby Elmach » Thu Apr 06, 2017 8:58 pm UTC

701
<<><<>><<>><<><>>>
<abb<aa>>
p(PDDp(PP))
2122222113

Code: Select all

*********
* * * ***
  * * * *

Image
prīmus (prīmī et bissecundī et prīmī bisprīmī)
701l.png
5 by 5 with one extra dot.
701l.png (1.36 KiB) Viewed 2027 times

Prime
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 9
Max Depth: 3

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Fri Apr 07, 2017 8:56 pm UTC

702
<><<>><<>><<>><<><<>>>
abbb<ab>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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

Re: Count up with recursive prime factorization

Postby Elmach » Fri Apr 07, 2017 11:41 pm UTC

703
<<><><>><<><><<>>>
<aaa><aab>
p(PPP)p(PPD)
211112211123

Code: Select all

***** *****
* * * * * *
          *

Image
prīmus terprīmī et prīmus (bisprīmī et secundī)
703al.png
5 by 4 exactly...
703al.png (1.27 KiB) Viewed 2019 times
703bl.png
but if I arrange it like this, you can see how similar the two factors are.
703bl.png (1.42 KiB) Viewed 2019 times

Semiprime (19 * 37)
Asymmetric
Not Alphabetic
Square-free, but recursively only tetradbiquadrate-free

Nodes: 9
Reversals: 11
Max Depth: 3
Smoothness: 37

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Sat Apr 08, 2017 10:21 pm UTC

704
<><><><><><><<<<>>>>
aaaaaad
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

User avatar
phillip1882
Posts: 111
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

Re: Count up with recursive prime factorization

Postby phillip1882 » Sat Apr 08, 2017 11:10 pm UTC

705
<<>><<<>>><<<>><<<>>>>
59.62% efficiency
good luck have fun

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Sat Apr 08, 2017 11:47 pm UTC

706
<><<<><><<<>>>>>
a<<aac>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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

Re: Count up with recursive prime factorization

Postby Elmach » Sun Apr 09, 2017 2:01 am UTC

707
<<><>><<><<><<>>>>
<aa><a<ab>>
spPPpPpPD1 or p(PP)p(Pp(Pp(P)))1 or spPPpPpPpPpPS1
2112212124

Code: Select all

*** *****
* * * ***
      * *
        *

Image
prīmus bisprīmī et prīmus (prīmī et prīmī (prīmī et secundī))
707al.png
7 by 4 with two extra dots.
707al.png (1.45 KiB) Viewed 2014 times

Semiprime (7 * 101)
Asymmetric
Not Alphabetic
Square-free, but recursively only cube-free

Nodes: 9
Reversals: 9
Max Depth: 4
Smoothness: 101
----
1Notes on this version of p-notation I've been developing
Spoiler:
It occurs to me that I've been using this notation for a while, and haven't really defined it anywhere (I think.). s, p, d, f, g, etc., are prefix binary functions (p*q, p*qth prime, etc.) and S, P, D, F, G, etc., are constants. (1 = "", 2 = <>, 3 = <<>>, 5 = <<<>>>, 11 = <<<<>>>>, etc..) This way, we can have a nonambiguous grammar without parentheses.

Of course, if I put parentheses afterwards, then the function just applies to the value in front, so s(Number) evaluates to Number, p(Number) evaluates to Numberth prime, etc.; also, in this case, assume sequences of terms evaluate to the product.

Without s, S, or parentheses, we can represent any prime with recursively no more than two factors. With parentheses, or with s, we can represent any number (where 1 is represented by the empty string).

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

Re: Count up with recursive prime factorization

Postby tomtom2357 » Fri Apr 14, 2017 10:56 am UTC

*sigh* We all want to have 709 don't we?
708
<><><<>><<<><>>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

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

Re: Count up with recursive prime factorization

Postby Elmach » Fri Apr 14, 2017 6:55 pm UTC

I just realized that 709 is a special number. That explains why the activity suddenly dropped.
----
709
<<<<<<<>>>>>>>
g (alphabet)
J (SPDFGHIJ/orbitals)
77 (7 up, then 7 down)

Code: Select all

*
*
*
*
*
*
*

Image
septimus
709l.png
7 by 7.
709l.png (3.79 KiB) Viewed 1993 times

709al.png
bad attempt of making circles
709al.png (4.51 KiB) Viewed 1990 times

Recursively prime/alphabetic atom. This sequence goes 1,2,3,5,11,31,127,709. The next one is 5381. According to OEIS, this is A007097.
Nodes: 7
Reversals: 1
Max Depth: 7
----


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