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### Re: Count up with recursive prime factorization

Posted: Sat Apr 01, 2017 7:35 pm UTC
691
<<<<>>><<<>>><<<>>>>
<ccc>

### Re: Count up with recursive prime factorization

Posted: Sun Apr 02, 2017 1:41 am UTC
692
<><><<><><><<<>>>>
72.66% efficiency

### Re: Count up with recursive prime factorization

Posted: Sun Apr 02, 2017 2:00 am UTC
693
<<>><<>><<><>><<<<>>>>
bb<aa>d

### Re: Count up with recursive prime factorization

Posted: Sun Apr 02, 2017 10:20 pm UTC
694
<><<<>><<<>><<>>>>
72.69% efficiency

### Re: Count up with recursive prime factorization

Posted: Mon Apr 03, 2017 2:15 am UTC
695
<<<>>><<><<<><>>>>
c<a<<aa>>>
Fp(Pd(PP))
33213114

Code: Select all

`* ****** * ****   ***    * *`

$\mathfrak{p}(\omega^{\omega^{\omega^{2}}+1}+\omega^{\omega})$
tertius et prīmus (prīmī et secundī bisprīmī)
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 4304 times

Spoiler:
A little happier with this version,
695bl2.png (3.44 KiB) Viewed 4302 times

or maybe this one.
695bl3.png (3.45 KiB) Viewed 4299 times

A version with arms
695b5al.png (1.56 KiB) Viewed 4296 times

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

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

### Re: Count up with recursive prime factorization

Posted: Mon Apr 03, 2017 10:17 am UTC
696
<><><><<>><<><<<>>>>
aaab<ac>

### Re: Count up with recursive prime factorization

Posted: Tue Apr 04, 2017 1:05 am UTC
697
<<<><>>><<<><<>>>>
<<aa>><<ab>>
d(PP)d(PD)
31133124

Code: Select all

`*** ****** **** * * *      *`

$\mathfrak{p}(\omega^{\omega^{\omega+1}}+\omega^{\omega^{2}})$
secundus bisprīmī et secundus (prīmī et secundī)

8 by 4 with one dot extra
697al.png (1.43 KiB) Viewed 4283 times

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

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

### Re: Count up with recursive prime factorization

Posted: Tue Apr 04, 2017 1:24 am UTC
698
<><<>><<<<>><<>>>>
ab<<bb>>

### Re: Count up with recursive prime factorization

Posted: Tue Apr 04, 2017 1:55 am UTC
699
<<>><<<>><<<><>>>>
b<b<<aa>>>
Dp(Dd(PP))
22323114

Code: Select all

`* ****** * ***  * ***    * *`

$\mathfrak{p}(\omega^{\omega^{\omega^{2}}+\omega}+\omega)$
secundus et prīmus (secundī et secundī bisprīmī)
6 by 5 exactly.
699l.png (1.59 KiB) Viewed 4272 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:
7 by 6 with seven unused dots, not optimal - EDIT: WRONG - this is 1165.
699l.png (1.67 KiB) Viewed 4281 times

### Re: Count up with recursive prime factorization

Posted: Wed Apr 05, 2017 11:36 pm UTC
700
<><><<<>>><<<>>><<><>>
59.56% efficiency

### Re: Count up with recursive prime factorization

Posted: Thu Apr 06, 2017 8:58 pm UTC
701
<<><<>><<>><<><>>>
<abb<aa>>
p(PDDp(PP))
2122222113

Code: Select all

`********** * * ***  * * * *`

$\mathfrak{p}(\omega^{\omega^{2}+\omega2+1})$
prīmus (prīmī et bissecundī et prīmī bisprīmī)
5 by 5 with one extra dot.
701l.png (1.36 KiB) Viewed 4260 times

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

Nodes: 9
Reversals: 9
Max Depth: 3

### Re: Count up with recursive prime factorization

Posted: Fri Apr 07, 2017 8:56 pm UTC
702
<><<>><<>><<>><<><<>>>
abbb<ab>

### Re: Count up with recursive prime factorization

Posted: Fri Apr 07, 2017 11:41 pm UTC
703
<<><><>><<><><<>>>
<aaa><aab>
p(PPP)p(PPD)
211112211123

Code: Select all

`***** ****** * * * * *          *`

$\mathfrak{p}(\omega^{\omega+2}+\omega^{3})$
prīmus terprīmī et prīmus (bisprīmī et secundī)
5 by 4 exactly...
703al.png (1.27 KiB) Viewed 4252 times
but if I arrange it like this, you can see how similar the two factors are.
703bl.png (1.42 KiB) Viewed 4252 times

Semiprime (19 * 37)
Asymmetric
Not Alphabetic

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

### Re: Count up with recursive prime factorization

Posted: Sat Apr 08, 2017 10:21 pm UTC
704
<><><><><><><<<<>>>>

### Re: Count up with recursive prime factorization

Posted: Sat Apr 08, 2017 11:10 pm UTC
705
<<>><<<>>><<<>><<<>>>>
59.62% efficiency

### Re: Count up with recursive prime factorization

Posted: Sat Apr 08, 2017 11:47 pm UTC
706
<><<<><><<<>>>>>
a<<aac>>

### Re: Count up with recursive prime factorization

Posted: 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

`*** ****** * * ***      * *        *`

$\mathfrak{p}(\omega^{\omega^{\omega+1}+1}+\omega^{2})$
prīmus bisprīmī et prīmus (prīmī et prīmī (prīmī et secundī))
7 by 4 with two extra dots.
707al.png (1.45 KiB) Viewed 4247 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).

### Re: Count up with recursive prime factorization

Posted: Fri Apr 14, 2017 10:56 am UTC
*sigh* We all want to have 709 don't we?
708
<><><<>><<<><>>>

### Re: Count up with recursive prime factorization

Posted: 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

`*******`

$\mathfrak{p}(\omega^{\omega^{\omega^{\omega^{\omega^{\omega}}}}})$
septimus
7 by 7.
709l.png (3.79 KiB) Viewed 4226 times

709al.png (4.51 KiB) Viewed 4223 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
----

### Re: Count up with recursive prime factorization

Posted: Wed Jun 19, 2019 4:15 pm UTC
710 = <><<>><<><><<>>>

### Re: Count up with recursive prime factorization

Posted: Wed Jun 19, 2019 5:22 pm UTC
711
slurpe
<<>><<>><<><<<<>>>>>

### Re: Count up with recursive prime factorization

Posted: Thu Jun 20, 2019 9:14 am UTC
712 = <><><><<<<>>><<<>>>>