Page 14 of 18

Re: Count up with recursive prime factorization

Posted: Sun Nov 30, 2014 1:37 am UTC
by Vytron
(.)(((..)))(.)


531

Re: Count up with recursive prime factorization

Posted: Sun Nov 30, 2014 2:13 am UTC
by Elmach
532
<><><<><>><<><><>> b-notation.

Before I go through the standard rigmarole I do with this (you know, ANALPHABETIC, ASYMMETRIC, COMPOSITE, <∴>-SMOOTH), I'd like to point out something interesting.
:<:><:.> dotted b-notation

If this were /2*3'd (so 768), then it would be "<><.><..><...>", where quotes represent string delimiters, not prime representations. An interesting pattern.

Image - levelset labynot
Image - boundary labynot

This is also laby-square (which minimizes area (49 = <:><:> =ImageImage) and perimeter (28 = <><><:> = :Image)).

Re: Count up with recursive prime factorization

Posted: Sun Nov 30, 2014 2:28 am UTC
by Vytron
<^>
<O>
V
<^^>
{o}
VV


533

Re: Count up with recursive prime factorization

Posted: Sun Nov 30, 2014 2:57 am UTC
by faubiguy
534
<><<>><<><><><<>>>
ab<aaab>
p1pp1p<p1p1p1pp1>
112221111123

Code: Select all

* * *******
  * * * * *
          *


Prime: No
Symmetrical: No
Alphabetical: No

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

Re: Count up with recursive prime factorization

Posted: Sun Nov 30, 2014 3:19 am UTC
by Elmach
535
<<<>>><<><<><>><>> b-notation
c<a<aa>a> alphabetic b-notation
3321211212 - faubian numerical cypher b-notation
3331121112 - standard form faubian numerical cypher b-notation
3321123212 - look-and-said form of standard form faubian numerical cypher b-notation
333111212 - inverted look-and-said form of standard form faubian numerical cypher b-notation
333111122 - inverted look-and-said form of first faubian numerical cypher b-notation
2312111221121112 - look-and-said form of first faubian numerical cypher b-notation

Image labinot level-set

COMPOSITE, ANALPHABETIC, ASYMMETRIC
Depth: <<>>
Smoothness: <<><<><>><>>, so not really at all
Length: <><<>><<>>. Personally, I prefer the half-length (<<>><<>>), because it is the number of p's in p-notation.

Re: Count up with recursive prime factorization

Posted: Sun Nov 30, 2014 3:21 am UTC
by Vytron
O
O((OOO))O


536

Post used to say
Spoiler:
<⊙>
<^>
O
(..)
v


535

Ninjaed editing correct count 536

Re: Count up with recursive prime factorization

Posted: Sun Nov 30, 2014 3:34 am UTC
by Elmach
537
<<>><<<<<>><>>>> - b-notation
b<<<ba>>> - alphabetic b-notation
225214 - faubian cypher b-notation
Image - level-set labinot
Image - better level-set labinot
Image - colored level-set labinot
Image - larger colored level-set labinot
Image - hypnotic larger colored level-set labinot

COMPOSITE, AN-ALPHABETIC, ASYMMETRIC
<<<>>>-deep
<<<<<>><>>>>-smooth
<><><> p's (::-length)

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 2:56 am UTC
by phillip1882
<><<<>><<><><>>> 538
efficiency: 66.93%

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 4:11 am UTC
by Vytron
(..)d(..)


539

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 4:58 am UTC
by faubiguy
540
<><><<>><<>><<>><<<>>>
aabbbc
p1p1pp1pp1pp1ppp1
111122222233

Code: Select all

* * * * * *
    * * * *
          *


Prime: No
Symmetrical: No
Alphabetical: Yes

Length: 22
Reversals: 11
Max Depth: 3
Factors: 6
Smoothness: 5
Necessary Brackets: 0

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 5:26 am UTC
by Vytron
[[[[]]]8[[[]]]]


541

(where the center is two circles, not an 8)

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 8:07 am UTC
by Elmach
faubiguy on page 7 wrote:271
<<><<><<<>>>>>
<a<ac>>

Reecer6 on page 7 wrote:I came up with 2926438, actually.

I think you have an extra '<' in the 7th position, and one missing from the 15th position. (It took quite a while to calculate that)

*2 difference
542 decimal
<><<><<><<<>>>>> standard benot
<><<<><<<>>>><>> alt. benot
a<a<ac>> alphabetic benot
a<<ac>a> alt. version
11212135 faubinumericypher benot
11313412 alt version
Image levelset labinot
[][[][[][[[]]]]]

COMPOSITE, ABALPHABETIC, ASYMMETRIC
<<<>>> - deep
<<><<><<<>>>>> - smooth (not smooth at all)
<<><>> - nodes (<>(:) length)

EDIT: Fixed my labinot one. I did Image originally, which is 202, a somewhat different number.

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 8:20 am UTC
by Vytron
faubiguy wrote:181
<<><<>><<><>>>
<ab<aa>>
(o⊙(..))





<••>



*3 difference.

<•>



<••>



543

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 8:28 am UTC
by Elmach
Vytron on page 1 wrote:pp<p1p1> (17)

phillip1882 wrote:p1p1p1p1
on the abiguity problem, another option is to use parenthesis.
6 = p(p1)p1, 7 = p(p1p1)


Yeah, what would work too. Though parenthesis give the illusion of multiplication (as in p*(p1p1)) while I think <>'s do a good job of showing recursion.

*32 difference = 544 - decimal
p1p1p1p1p1pp<p1p1> - penot
<><><><><><<<><>>> - benot
aaaaa<<aa>> - alph. benot
11111111113113 - faubinumericypher benot
(10)1132113 - look-and-say of faubinumericypher benot
Image - level set labinot

::
◠◠
<••>
◡◡

ABALPHABETIC, ASYMMETRIC, COMPOSITE
<<>>-deep
<<<><>>>-smooth (quite smooth for a large number!)
<><<<>>>-nodes (<><<<>>><> length)
<<>><<>> nodes (<<>><><<>> length)

EDIT: 32 is 2^5, not 2^6. Whoops. Original labyrinthine notations: (all the others are in the same format)
Spoiler:
Image - levelset labinot
Image - another version
Image - compact version

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 8:47 am UTC
by Vytron
Vytron wrote:
Λ
O
V
ΛΛ
O
ΛΛ
O
VV
VV


327


Difference of /3 *5

ΛΛ
O
VV
ΛΛ
O
ΛΛ
O
VV
VV


545

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 2:22 pm UTC
by phillip1882
<><<>><<><>><<><<>>> 546
efficiency: 63.47

Re: Count up with recursive prime factorization

Posted: Mon Dec 01, 2014 11:21 pm UTC
by Vytron

^^
o

Λ


VVV


547

Re: Count up with recursive prime factorization

Posted: Tue Dec 02, 2014 1:05 am UTC
by faubiguy
548
<><><<<>><<<<>>>>>
aa<bd>
p1p1p<pp1pppp1>
11113245

Code: Select all

* * ***
    * *
    * *
      *
      *


Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 7
Max Depth: 5
Factors: 3
Smoothness: 137
Necessary Brackets: 2

Re: Count up with recursive prime factorization

Posted: Tue Dec 02, 2014 1:19 am UTC
by Vytron

<^>

{o}
v


549

Re: Count up with recursive prime factorization

Posted: Tue Dec 09, 2014 1:20 am UTC
by Elmach
550 - decimal 11, 2, 2, 5, 5
<><<<>>><<<<>>>><<<>>><> - benot
acdca - alph. benot
1133443311 - faubinumericypher benot
ALPHABETIC, SYMMETRIC, COMPOSITE
O
(⊙)
«⊙»
(⊙)
O


<><>-deep
<<<<>>>>-smooth (quite smooth for a large number!)
<><<>><> nodes (<><><><<>> length)

Re: Count up with recursive prime factorization

Posted: Tue Dec 09, 2014 2:09 am UTC
by faubiguy
551
<<><><>><<><<<>>>>
<aaa><ac>
p<p1p1p1>p<p1ppp1>
2111122134

Code: Select all

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


Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 9
Max Depth: 4
Factors: 2
Smoothness: 29
Necessary Brackets: 4

Re: Count up with recursive prime factorization

Posted: Sat Dec 20, 2014 9:45 pm UTC
by phillip1882
552 = <><><><<>><<<>><<>>>
efficiency: 63.53%

Re: Count up with recursive prime factorization

Posted: Sat Dec 20, 2014 10:05 pm UTC
by Vytron
Yay! Finally get to make an odd number!

d


(((〇)))


553

Re: Count up with recursive prime factorization

Posted: Sun Dec 21, 2014 1:28 pm UTC
by faubiguy
554
<><<<<<><>>>>>
a<<<<aa>>>>
p1p<p<p<p<p1p1>>>>
115115

Code: Select all

* ***
  ***
  ***
  ***
  * *


Prime: No
Symmetrical: No
Alphabetical: No

Length: 14
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 277
Necessary Brackets: 8

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 3:56 am UTC
by Vytron
۞
((۝))
Λ
۝
۞
۝
V


555

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 4:15 am UTC
by faubiguy
556
<><><<><<<><>>>>
aa<a<<aa>>>
p1p1p<p1p<p<p1p1>>>
1111213114

Code: Select all

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


Prime: No
Symmetrical: No
Alphabetical: No

Length: 16
Reversals: 9
Max Depth: 4
Factors: 3
Smoothness: 139
Necessary Brackets: 6

Vytron wrote:Did you do the same number that I did? D:

Fixed. I forgot to add 1 to the number in the previous post.

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 7:43 am UTC
by Elmach
You skipped 555 :(


Vytron wrote:

^

۞
v


111

Post used to say
Spoiler:
^
<◠>
<<◇>>

V


109

Times five ((())).

So
⊙<∞۞>(⊙)
Is 555

phillip1882 wrote:<><<>><<<><>>> 102

Eth prime.
So
<<><<>><<<><>>>>
Is 557

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 11:36 am UTC
by faubiguy
558
<><<>><<>><<<<<>>>>>
abbe
p1pp1pp1ppppp1
11222255

Code: Select all

* * * *
  * * *
      *
      *
      *


Prime: No
Symmetrical: No
Alphabetical: Yes

Length: 20
Reversals: 7
Max Depth: 5
Factors: 4
Smoothness: 31
Necessary Brackets: 0

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 6:31 pm UTC
by Vytron
Elmach wrote:You skipped 555 :(


What? No! You just checked my post too early :P

<^>
( 8 )
V
<^>
<O>
V


559

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 7:26 pm UTC
by faubiguy
560
<><><><><<<>>><<><>>
aaaac<aa>
p1p1p1p1ppp1p<p1p1>
11111111332112

Code: Select all

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


Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 13
Max Depth: 3
Factors: 6
Smoothness: 7
Necessary Brackets: 2

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 7:32 pm UTC
by Vytron
ΛΛΛ
o
VVV
[[◇◇]]
۞


561

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 7:42 pm UTC
by faubiguy
562
<><<><><<>><<<>>>>
a<aabc>
p1p<p1p1pp1ppp1>
1121112234

Code: Select all

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


Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 9
Max Depth: 4
Factors: 2
Smoothness: 281
Necessary Brackets: 2

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 8:05 pm UTC
by Vytron
<(⊙⊙⊙)>


563

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 8:12 pm UTC
by faubiguy
564
<><><<>><<<>><<<>>>>
aab<bc>
p1p1pp1p<pp1ppp1>
1111223234

Code: Select all

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


Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 9
Max Depth: 4
Factors: 4
Smoothness: 47
Necessary Brackets: 2

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 8:54 pm UTC
by Vytron
((۝))

o


۞



565

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 9:37 pm UTC
by faubiguy
566
<><<<><<>><<>>>>
a<<abb>>
p1p<p<p1pp1pp1>>
11312224

Code: Select all

* *****
  *****
  * * *
    * *


Prime: No
Symmetrical: No
Alphabetical: No

Length: 16
Reversals: 7
Max Depth: 4
Factors: 2
Smoothness: 283
Necessary Brackets: 4

Re: Count up with recursive prime factorization

Posted: Mon Dec 22, 2014 9:58 pm UTC
by Vytron
⊙⊙
(..)
⊙⊙


567

Re: Count up with recursive prime factorization

Posted: Tue Dec 23, 2014 12:40 am UTC
by faubiguy
568
<><><><<><><<<>>>>
aaa<aac>
p1p1p1p<p1p1ppp1>
111111211134

Code: Select all

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


Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 11
Max Depth: 4
Factors: 4
Smoothness: 71
Necessary Brackets: 2

Re: Count up with recursive prime factorization

Posted: Tue Dec 23, 2014 1:02 am UTC
by Vytron
Λ
۝ ۝
Λ
۝
۞
V
O
V


569

Re: Count up with recursive prime factorization

Posted: Tue Dec 23, 2014 1:49 am UTC
by faubiguy
570
<><<>><<<>>><<><><>>
abc<aaa>
p1pp1ppp1p<p1p1p1>
112233211112

Code: Select all

* * * *****
  * * * * *
    *     


Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 11
Max Depth: 3
Factors: 4
Smoothness: 19
Necessary Brackets: 2