Count up with recursive prime factorization
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 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
611
<<><<>>><<<>><<<>>>>
<ab><bc>
<<><<>>><<<>><<<>>>>
<ab><bc>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
 emlightened
 Posts: 42
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
612
<><><<>><<>><<<><>>>
ab<<aa>>ba
@faubi: That looks fine.
<><><<>><<>><<<><>>>
ab<<aa>>ba
@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."
"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."
Re: Count up with recursive prime factorization
613
<<><><><><<><>>>
<aaaa<aa>>
p<p1p1p1p1p<p1p1>>
211111112113
Prime: Yes
Symmetrical: Yes
Alphabetical: No
Length: 16
Reversals: 11
Max Depth: 3
Factors: 1
Smoothness: 613
Necessary Brackets: 4
<<><><><><<><>>>
<aaaa<aa>>
p<p1p1p1p1p<p1p1>>
211111112113
Code: Select all
***********
* * * * ***
* *
Prime: Yes
Symmetrical: Yes
Alphabetical: No
Length: 16
Reversals: 11
Max Depth: 3
Factors: 1
Smoothness: 613
Necessary Brackets: 4
 emlightened
 Posts: 42
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
614
<><<<>><<>><<><>>>
a<bb<aa>>
<><<<>><<>><<><>>>
a<bb<aa>>
██████████████████████████████████████████████████████████████████████████████████████████████████████
"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."
"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."
Re: Count up with recursive prime factorization
615
<<>><<<>>><<<><<>>>>
bc<<ab>>
pp1ppp1p<p<p1pp1>>
22333124
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 7
Max Depth: 4
Factors: 3
Smoothness: 41
Necessary Brackets: 4
<<>><<<>>><<<><<>>>>
bc<<ab>>
pp1ppp1p<p<p1pp1>>
22333124
Code: Select all
* * ***
* * ***
* * *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 7
Max Depth: 4
Factors: 3
Smoothness: 41
Necessary Brackets: 4
 emlightened
 Posts: 42
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
616
<><><><<><>><<<<>>>>
aaa<aa>d
<><><><<><>><<<<>>>>
aaa<aa>d
██████████████████████████████████████████████████████████████████████████████████████████████████████
"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."
"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."

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
617
<<<><<>><<<>>>>>
<<abc>>
<<<><<>><<<>>>>>
<<abc>>
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
 emlightened
 Posts: 42
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
618
<><<>><<<>><<>><<>>>
ab<bbb>
<><<>><<<>><<>><<>>>
ab<bbb>
██████████████████████████████████████████████████████████████████████████████████████████████████████
"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."
"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."
Re: Count up with recursive prime factorization
619
<<><<>><<><><>>>
<ab<aaa>>
p<p1pp1p<p1p1p1>>
2122211113
Prime: Yes
Symmetrical: No
Alphabetical: No
Length: 16
Reversals: 9
Max Depth: 3
Factors: 1
Smoothness: 619
Necessary Brackets: 4
<<><<>><<><><>>>
<ab<aaa>>
p<p1pp1p<p1p1p1>>
2122211113
Code: Select all
*********
* * *****
* * * *
Prime: Yes
Symmetrical: No
Alphabetical: No
Length: 16
Reversals: 9
Max Depth: 3
Factors: 1
Smoothness: 619
Necessary Brackets: 4

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
620
<><><<<>>><<<<<>>>>>
aace
<><><<<>>><<<<<>>>>>
aace
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
621
<<>><<>><<>><<<>><<>>>
bbb<bb>
pp1pp1pp1p<pp1pp1>
2222223223
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 9
Max Depth: 3
Factors: 4
Smoothness: 23
Necessary Brackets: 2
<<>><<>><<>><<<>><<>>>
bbb<bb>
pp1pp1pp1p<pp1pp1>
2222223223
Code: Select all
* * * ***
* * * * *
* *
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 9
Max Depth: 3
Factors: 4
Smoothness: 23
Necessary Brackets: 2

 Posts: 563
 Joined: Tue Jul 27, 2010 8:48 am UTC
Re: Count up with recursive prime factorization
<><<><><><><><>>
a<aaaaaa>
P(w^{6}+1)
a<aaaaaa>
P(w^{6}+1)
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
Re: Count up with recursive prime factorization
623
<<><>><<><><><<>>>
<aa><aaab>
p<p1p1>p<p1p1p1pp1>
211221111123
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 11
Max Depth: 3
Factors: 2
Smoothness: 89
Necessary Brackets: 4
<<><>><<><><><<>>>
<aa><aaab>
p<p1p1>p<p1p1p1pp1>
211221111123
Code: Select all
*** *******
* * * * * *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 11
Max Depth: 3
Factors: 2
Smoothness: 89
Necessary Brackets: 4
 emlightened
 Posts: 42
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
624
<><><><><<>><<><<>>>
aaaab<ab>
<><><><><<>><<><<>>>
aaaab<ab>
██████████████████████████████████████████████████████████████████████████████████████████████████████
"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."
"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."
Re: Count up with recursive prime factorization
625
<<<>>><<<>>><<<>>><<<>>>
cccc
ppp1ppp1ppp1ppp1
33333333
Prime: No
Symmetrical: Yes
Alphabetical: Yes
Length: 24
Reversals: 7
Max Depth: 3
Factors: 4
Smoothness: 5
Necessary Brackets: 0
Another integer power.
<<<>>><<<>>><<<>>><<<>>>
cccc
ppp1ppp1ppp1ppp1
33333333
Code: Select all
* * * *
* * * *
* * * *
Prime: No
Symmetrical: Yes
Alphabetical: Yes
Length: 24
Reversals: 7
Max Depth: 3
Factors: 4
Smoothness: 5
Necessary Brackets: 0
Another integer power.
 emlightened
 Posts: 42
 Joined: Sat Sep 26, 2015 9:35 pm UTC
 Location: Somewhere cosy.
Re: Count up with recursive prime factorization
626
<><<><><><<><<>>>>
a<c<ab>>
<><<><><><<><<>>>>
a<c<ab>>
██████████████████████████████████████████████████████████████████████████████████████████████████████
"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."
"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."
Re: Count up with recursive prime factorization
627
<<>><<<<>>>><<><><>>
bd<aaa>
pp1pppp1p<p1p1p1>
2244211112
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 9
Max Depth: 4
Factors: 3
Smoothness: 19
Necessary Brackets: 2
<<>><<<<>>>><<><><>>
bd<aaa>
pp1pppp1p<p1p1p1>
2244211112
Code: Select all
* * *****
* * * * *
*
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 20
Reversals: 9
Max Depth: 4
Factors: 3
Smoothness: 19
Necessary Brackets: 2
Re: Count up with recursive prime factorization
The number is 628.
Here's a new notation!
103242301
423230101
In the more standard bracketnotation,
<><<<><<>><>>><>
<<<<>><><>>><><>
1131221311 look and see notation
4211131111 also look and see notation
symmetric, not alphabetic, composite
Halflength: 7
Reversals: 9
Depth: 4
in pink ordinals (fora, echo), whatever they are.
(note: boundary notation, not levelset. 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.
Here's a new notation!
103242301
423230101
In the more standard bracketnotation,
<><<<><<>><>>><>
<<<<>><><>>><><>
1131221311 look and see notation
4211131111 also look and see notation
symmetric, not alphabetic, composite
Halflength: 7
Reversals: 9
Depth: 4
in pink ordinals (fora, echo), whatever they are.
(note: boundary notation, not levelset. 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.
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
629
<<<><>>><<><><<>>>
65.9% efficiency
<<<><>>><<><><<>>>
65.9% efficiency
good luck have fun
Re: Count up with recursive prime factorization
630
<><<>><<>><<<>>><<><>>
abbc<aa>
p1pp1pp1ppp1p<p1p1>
112222332112
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 11
Max Depth: 3
Factors: 5
Smoothness: 7
Necessary Brackets: 2
<><<>><<>><<<>>><<><>>
abbc<aa>
p1pp1pp1ppp1p<p1p1>
112222332112
Code: Select all
* * * * ***
* * * * *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 22
Reversals: 11
Max Depth: 3
Factors: 5
Smoothness: 7
Necessary Brackets: 2
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
631
<<<<>>><<<>><<>>>>
65.92% efficiency
<<<<>>><<<>><<>>>>
65.92% efficiency
good luck have fun
Re: Count up with recursive prime factorization
632
<ad>aaa
<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.
Re: Count up with recursive prime factorization
633
<<>><<<<>><<<>>>>>
b<<bc>>
pp1p<p<pp1ppp1>>
224235
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 211
Necessary Brackets: 4
<<>><<<<>><<<>>>>>
b<<bc>>
pp1p<p<pp1ppp1>>
224235
Code: Select all
* ***
* ***
* *
* *
*
Prime: No
Symmetrical: No
Alphabetical: No
Length: 18
Reversals: 5
Max Depth: 5
Factors: 2
Smoothness: 211
Necessary Brackets: 4
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
634
<><<><<>><<<<>>>>>
65.95% efficiency
<><<><<>><<<<>>>>>
65.95% efficiency
good luck have fun
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
636
<><><<>><<><><><>>
65.96% efficiency
<><><<>><<><><><>>
65.96% efficiency
good luck have fun
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
638
<><<<<>>>><<><<<>>>>
64.35% efficiency
<><<<<>>>><<><<<>>>>
64.35% efficiency
good luck have fun
Re: Count up with recursive prime factorization
639
<<>><<><><<<>>>><<>>
<<>><<><><<<>>>><<>>
I don't know what I'm doing.
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
640
<><><><><><><><<<>>>
64.36% efficiency.
<><><><><><><><<<>>>
64.36% efficiency.
good luck have fun
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
642
<><<>><<><><<><>>>
66.01% efficiency
<><<>><<><><<><>>>
66.01% efficiency
good luck have fun
Re: Count up with recursive prime factorization
643
<<<>><<>><<><<>>>>
<<<>><<>><<><<>>>>
Re: Count up with recursive prime factorization
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;
ω^{ω2} + ω^{2} + 2
I'm wondering, how many people are using a program, and how many are doing this manually?
Re: Count up with recursive prime factorization
645
<<>><<<>>><<><<><>>>
bc<a<aa>>
pp1ppp1p<p1p<p1p1>>
2233212113
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
<<>><<<>>><<><<><>>>
bc<a<aa>>
pp1ppp1p<p1p<p1p1>>
2233212113
Code: Select all
* * *****
* * * ***
* * *
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
Re: Count up with recursive prime factorization
646
<><<<><>>><<><><>>
<><<<><>>><<><><>>
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
647
<<><<<<><>>>>>
69.94% efficiency
<<><<<<><>>>>>
69.94% efficiency
good luck have fun
Re: Count up with recursive prime factorization
648
<><><><<>><<>><<>><<>>
<><><><<>><<>><<>><<>>
 phillip1882
 Posts: 145
 Joined: Fri Jun 14, 2013 9:11 pm UTC
 Location: geogia
 Contact:
Re: Count up with recursive prime factorization
649
<<<<>>>><<<<><>>>>
66.07% efficiency
<<<<>>>><<<<><>>>>
66.07% efficiency
good luck have fun
Re: Count up with recursive prime factorization
650
<><<<>>><<<>>><<><<>>>
<><<<>>><<<>>><<><<>>>
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