## Count up with recursive prime factorization

For all your silly time-killing forum games.

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AarexTiaokhiao
Posts: 35
Joined: Mon Nov 03, 2014 9:33 pm UTC

### Re: Count up with recursive prime factorization

491
<<><<<>><<<>>>>>
(o(⊙(⊙)))
(a(b(b)))
12234345
I QUIT

phillip1882
Posts: 141
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

just for giggles i created a recursive number program.

Code: Select all

`recurse = [""]*1000000recurse[2] = "<>"n = 2p = 1while n < len(recurse):   for v in range(2,int(len(recurse)/n)):      if recurse[v] != "":         recurse[v*n] = recurse[v] +recurse[n]   n += 1   while n<len(recurse) and recurse[n] != "":      n += 1   if n == len(recurse):      break   p += 1   recurse[n] = "<" +recurse[p] +">"print(recurse[492])`

492 = <><><<>><<<><<>>>>
efficiency: 64.55
good luck have fun

AarexTiaokhiao
Posts: 35
Joined: Mon Nov 03, 2014 9:33 pm UTC

### Re: Count up with recursive prime factorization

493
<<<><>>><<<>><<>>>
((oo))(⊙⊙)
((aa))(bb)
123312323

Code: Select all

`*** ****** * ** * * *`
I QUIT

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

494
<><<><<>>><<><><>>
a<ab><aaa>
p1p<p1pp1>p<p1p1p1>
112123211112

Code: Select all

`* *** *****  * * * * *    *      `

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 11
Max Depth: 3
Factors: 3
Smoothness: 19
Necessary Brackets: 4

AarexTiaokhiao
Posts: 35
Joined: Mon Nov 03, 2014 9:33 pm UTC

### Re: Count up with recursive prime factorization

495
<<>><<>><<<>>><<<<>>>>
^
(OXOX⊙X(⊙))
v

⊙⊙(⊙)((⊙))
bbcd
12121231234

Code: Select all

`* * * ** * * *  * * *    * *`
I QUIT

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

496
<><><><><<<<<>>>>>
aaaae
p1p1p1p1ppppp1
1111111155

Code: Select all

`* * * * *        *        *        *        *`

Prime: No
Symmetrical: Yes
Alphabetical: Yes

Length: 18
Reversals: 9
Max Depth: 5
Factors: 5
Smoothness: 31
Necessary Brackets: 0

AarexTiaokhiao
Posts: 35
Joined: Mon Nov 03, 2014 9:33 pm UTC

### Re: Count up with recursive prime factorization

497
7{2{1}*2{1}}*71{2{1}*2{1}*5{3{2{1}}}}
<<><>><<><><<<>>>>
(oo)(oo(⊙))
<aa><aab>
12212223

Code: Select all

`*** ****** * * * *        *`
I QUIT

firesoul31
Posts: 93
Joined: Wed Feb 27, 2013 10:30 pm UTC

### Re: Count up with recursive prime factorization

p1pp1pp<pp1pp1>
<><<>><<<<>><<>>>>
498

phillip1882
Posts: 141
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

<<<<>>><<><><>>> 499
efficiency: 66.52%
good luck have fun

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

500
<><><<<>>><<<>>><<<>>>
aaccc
p1p1ppp1ppp1ppp1
1111333333

Code: Select all

`* * * * *    * * *    * * *`

Prime: No
Symmetrical: Yes
Alphabetical: Yes

Length: 22
Reversals: 9
Max Depth: 3
Factors: 5
Smoothness: 5
Necessary Brackets: 0

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

^

<^>
<O>
VV

501

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

502
<><<><<>><<>><<>>>
a<abbb>
p1p<p1pp1pp1pp1>
1121222223

Code: Select all

`* *******  * * * *    * * *`

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 9
Max Depth: 3
Factors: 2
Smoothness: 251
Necessary Brackets: 2

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

<^>
۝۞۝
۝
<
v>

503

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

504
<><><><<>><<>><<><>>
aaabb<aa>
p1p1p1pp1pp1p<p1p1>
11111122222112

Code: Select all

`* * * * * ***      * * * *`

Prime: No
Symmetrical: No
Alphabetical: No

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

(Even after 3 weeks, this thread seems to be going much faster than 'Count up in a somewhat complex way')

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

Λ

^
o

VV
[[[]]]

505

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

506
<><<<<>>>><<<>><<>>>
p1pppp1p<pp1pp1>
11443223

Code: Select all

`* * ***  * * *  * * *  *    `

Prime: No
Symmetrical: No
Alphabetical: No

Length: 20
Reversals: 7
Max Depth: 4
Factors: 3
Smoothness: 23
Necessary Brackets: 2

phillip1882
Posts: 141
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

<<>><<><<>>><<><<>>> 507
efficiency: 63.03%
good luck have fun

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

### Re: Count up with recursive prime factorization

Vytron on page 7 wrote:Just fixed all my counts of previous page.

O
<<<<<۝>>>>>

254

O
<<<<<۝>>>>>
O

508

afa (abc-ext. b-not.)
<><<<<<<>>>>>><> (st. b-not.)

Code: Select all

`* * *  *  *  *  *  *`

Symmetric, alphabetic, and composite. 27-1-smooth, though, so not really smooth at all. (a=2,b=3,c=5,d=11,e=31,f=127)

(Labyrinth-not.)

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

509
<<<<<>>><<<>>>>>
<<cc>>
p<p<ppp1ppp1>>
5335

Code: Select all

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

Prime: Yes
Symmetrical: Yes
Alphabetical: No

Length: 16
Reversals: 3
Max Depth: 5
Factors: 1
Smoothness: 509
Necessary Brackets: 4

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

Vytron wrote:

〇〇
<<〇>>
<<〇〇>>

340

(/2 *3)

<〇>
<<〇>>
<<〇〇>>

510

phillip1882
Posts: 141
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

<<><>><<<>><<><>>> 511
efficiency: 64.77%
good luck have fun

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

512
<><><><><><><><><>
aaaaaaaaa
p1p1p1p1p1p1p1p1p1
111111111111111111

Code: Select all

`* * * * * * * * *`

Prime: No
Symmetrical: Yes
Alphabetical: Yes

Length: 18
Reversals: 17
Max Depth: 1
Factors: 9
Smoothness: 2
Necessary Brackets: 0

Power of 2

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

<>
<
><><>

513

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

514
<><<<<>>><<<<>>>>>
a<cd>
p1p<ppp1pppp1>
114345

Code: Select all

`* ***  * *  * *  * *    *`

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 257
Necessary Brackets: 2

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

515.png (25.18 KiB) Viewed 6707 times

In 3D phlip's notation.

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

### Re: Count up with recursive prime factorization

I don't think you should have put the five in front of the prime-twenty-seven, because that looks really weird and it makes me think the 3d-notation is claiming that the number is a prime-bubble when it is really two bubbles in front of each other.

516

<><><<>><<><<><>>> (b-not.)
COLON SUN(OH(COLON)) (AB. b-not.)
(Labyrinthine notation)

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

Elmach wrote:it is really two bubbles in front of each other.

That's the idea! This is a sideway representation of the number:

515side.png (33.7 KiB) Viewed 6671 times

The smaller sphere is not inside the bigger one! The problem with this sideway representation is that it isn't 3D (i.e. those circles could be represented with 2D shapes, whereas tridimensionality is necessary to see the spheres are in front of each other.)

ΛΛΛ
o
VVV

<<◇>>

517

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

### Re: Count up with recursive prime factorization

518

<><:><:<<>>> (colonned b-notation)
(boundary labyrinthine notation)
(level set lab. not)
(compacter b-lab. not.)
(that one in ls-lab. not.)

I think that is the most compact (EDIT: perimeterwise) you can get in labyrinthine notation. (Clearly every ls-lab.not. gives rise to a b-lab.not. of the same structure, so it doesn't matter if you use one or the other; although b-lab is larger, I think ls-lab is more readable.)
EDIT: No; clearly, rotating the left p12 will result in less space used, minimizing area. This would be true if it were half the size. This is false.
Clearly, it has to be at least five(ls-lab)/eleven (b-lab)-tall to hold the <<<>>> bit.

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

That gives me an idea for a notation, will use it first time I have the chance.

<〇>
Λ
〇〇〇
<<〇>>
V

519

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

### Re: Count up with recursive prime factorization

Alright! Can't wait to see it.

520:

<><<<>>><><<><<>>> (b-notation)
Asymmetric, analphabetic, composite, <<><<>>>-smooth, which is quite smooth, actually!
If this were 260, then it would be nice. But it isn't, so it has this sort of boundary-labyrinthine-notation. (In level-set labyrinthine, it is , of course.)

Something about laby-not. makes fives () much larger than sevens (). Odd. (It's because going deeper is more expensive than making another. For small numbers.)
Last edited by Elmach on Sat Nov 29, 2014 7:14 am UTC, edited 2 times in total.

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

521.png (25.77 KiB) Viewed 6610 times

Oh well, doesn't look at all how I imagined it.

The idea is to make a cube-like visualization of a Labyrinth representation, by having a maze in each face. Perhaps with a more complex design...

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

### Re: Count up with recursive prime factorization

Alright then, would 523 be a prime that would work better?

522 - composite, analphabetic, asymmetric
<><<>><<>><<><<<>>>> - bracket notation
abb<ac> - alphabetic bracket notation
- Labyrinthine notation, level-set mode.
- Labyrinthine notation, boundary mode.

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

523.png (25.58 KiB) Viewed 6594 times

Um... well, at least it looks somewhat more inspired.

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

### Re: Count up with recursive prime factorization

Well... 525 must be better, right? (assuming smooth numbers are good.)

524:

<><<><><><><>><> (b-notation)

SYMMETRIC, but composite, and analphabetic.

Labyrinthine
Last edited by Elmach on Sat Nov 29, 2014 8:52 am UTC, edited 3 times in total.

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

525.png (27.98 KiB) Viewed 6562 times

Still doesn't look like a labyrinth at all D:

Anyway, returning to text on next post...

phillip1882
Posts: 141
Joined: Fri Jun 14, 2013 9:11 pm UTC
Location: geogia
Contact:

### Re: Count up with recursive prime factorization

<><<><><><<><>>> 526
efficiency: 66.81%
good luck have fun

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

527
<<<><>>><<<<<>>>>>
<<aa>>e
p<p<p1p1>>ppppp1
311355

Code: Select all

`*** **** ** * *    *    *`

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 31
Necessary Brackets: 4

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

### Re: Count up with recursive prime factorization

528
<><><><><<>><<<<>>>> in b-notation
aaaabd in alphabetic b-notation
in level-set labyrinthine notation
in boundary l-notation

alphabetic, asymmetric, and composite. d-smooth.

Vytron
Posts: 429
Joined: Mon Oct 19, 2009 10:11 am UTC
Location: The Outside. I use She/He/Her/His/Him as gender neutral pronouns :P

### Re: Count up with recursive prime factorization

"<o> <o>"
"<o> <o>"

529

Where I am using quotes as another pair of angle brackets.

faubiguy
Posts: 15
Joined: Sun Aug 11, 2013 9:20 am UTC

### Re: Count up with recursive prime factorization

530
<><<<>>><<><><><>>
ac<aaaa>
p1ppp1p<p1p1p1p1>
113321111112

Code: Select all

`* * *******  * * * * *  *        `

Prime: No
Symmetrical: No
Alphabetical: No

Length: 18
Reversals: 11
Max Depth: 3
Factors: 3
Smoothness: 53
Necessary Brackets: 2

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