### Re: Count up with recursive prime factorization

Posted:

**Sat Apr 01, 2017 7:35 pm UTC**691

<<<<>>><<<>>><<<>>>>

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<ccc>

Forums for the webcomic xkcd.com

http://forums3.xkcd.com/

Page **18** of **18**

Posted: **Sat Apr 01, 2017 7:35 pm UTC**

691

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<ccc>

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<ccc>

Posted: **Sun Apr 02, 2017 1:41 am UTC**

692

<><><<><><><<<>>>>

72.66% efficiency

<><><<><><><<<>>>>

72.66% efficiency

Posted: **Sun Apr 02, 2017 2:00 am UTC**

693

<<>><<>><<><>><<<<>>>>

bb<aa>d

<<>><<>><<><>><<<<>>>>

bb<aa>d

Posted: **Sun Apr 02, 2017 10:20 pm UTC**

694

<><<<>><<<>><<>>>>

72.69% efficiency

<><<<>><<<>><<>>>>

72.69% efficiency

Posted: **Mon Apr 03, 2017 2:15 am UTC**

695

<<<>>><<><<<><>>>>

c<a<<aa>>>

Fp(Pd(PP))

33213114

tertius et prīmus (prīmī et secundī bisprīmī)

**Spoiler:**

Semiprime

Asymmetric

Not Alphabetic

square-free, but recursively only cube-free

Nodes: 9

Reversals: 7

Max Depth: 4

Smoothness: 139

<<<>>><<><<<><>>>>

c<a<<aa>>>

Fp(Pd(PP))

33213114

Code: Select all

`* *****`

* * ***

* ***

* *

tertius et prīmus (prīmī et secundī bisprīmī)

Semiprime

Asymmetric

Not Alphabetic

square-free, but recursively only cube-free

Nodes: 9

Reversals: 7

Max Depth: 4

Smoothness: 139

Posted: **Mon Apr 03, 2017 10:17 am UTC**

696

<><><><<>><<><<<>>>>

aaab<ac>

<><><><<>><<><<<>>>>

aaab<ac>

Posted: **Tue Apr 04, 2017 1:05 am UTC**

697

<<<><>>><<<><<>>>>

<<aa>><<ab>>

d(PP)d(PD)

31133124

secundus bisprīmī et secundus (prīmī et secundī)

Semiprime

Asymmetric

Not Alphabetic

Square-free, but recursively only cube-free

Nodes: 9

Reversals: 7

Max Depth: 4

Smoothness: 41

<<<><>>><<<><<>>>>

<<aa>><<ab>>

d(PP)d(PD)

31133124

Code: Select all

`*** ***`

*** ***

* * * *

*

secundus bisprīmī et secundus (prīmī et secundī)

Semiprime

Asymmetric

Not Alphabetic

Square-free, but recursively only cube-free

Nodes: 9

Reversals: 7

Max Depth: 4

Smoothness: 41

Posted: **Tue Apr 04, 2017 1:24 am UTC**

698

<><<>><<<<>><<>>>>

ab<<bb>>

<><<>><<<<>><<>>>>

ab<<bb>>

Posted: **Tue Apr 04, 2017 1:55 am UTC**

699

<<>><<<>><<<><>>>>

b<b<<aa>>>

Dp(Dd(PP))

22323114

secundus et prīmus (secundī et secundī bisprīmī)

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:**

<<>><<<>><<<><>>>>

b<b<<aa>>>

Dp(Dd(PP))

22323114

Code: Select all

`* *****`

* * ***

* ***

* *

secundus et prīmus (secundī et secundī bisprīmī)

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.

Posted: **Wed Apr 05, 2017 11:36 pm UTC**

700

<><><<<>>><<<>>><<><>>

59.56% efficiency

<><><<<>>><<<>>><<><>>

59.56% efficiency

Posted: **Thu Apr 06, 2017 8:58 pm UTC**

701

<<><<>><<>><<><>>>

<abb<aa>>

p(PDDp(PP))

2122222113

prīmus (prīmī et bissecundī et prīmī bisprīmī)

Prime

Asymmetric

Not Alphabetic

Square-free, but recursively only cube-free

Nodes: 9

Reversals: 9

Max Depth: 3

<<><<>><<>><<><>>>

<abb<aa>>

p(PDDp(PP))

2122222113

Code: Select all

`*********`

* * * ***

* * * *

prīmus (prīmī et bissecundī et prīmī bisprīmī)

Prime

Asymmetric

Not Alphabetic

Square-free, but recursively only cube-free

Nodes: 9

Reversals: 9

Max Depth: 3

Posted: **Fri Apr 07, 2017 8:56 pm UTC**

702

<><<>><<>><<>><<><<>>>

abbb<ab>

<><<>><<>><<>><<><<>>>

abbb<ab>

Posted: **Fri Apr 07, 2017 11:41 pm UTC**

703

<<><><>><<><><<>>>

<aaa><aab>

p(PPP)p(PPD)

211112211123

prīmus terprīmī et prīmus (bisprīmī et secundī)

Semiprime (19 * 37)

Asymmetric

Not Alphabetic

Square-free, but recursively only~~tetrad~~biquadrate-free

Nodes: 9

Reversals: 11

Max Depth: 3

Smoothness: 37

<<><><>><<><><<>>>

<aaa><aab>

p(PPP)p(PPD)

211112211123

Code: Select all

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

* * * * * *

*

prīmus terprīmī et prīmus (bisprīmī et secundī)

Semiprime (19 * 37)

Asymmetric

Not Alphabetic

Square-free, but recursively only

Nodes: 9

Reversals: 11

Max Depth: 3

Smoothness: 37

Posted: **Sat Apr 08, 2017 10:21 pm UTC**

704

<><><><><><><<<<>>>>

aaaaaad

<><><><><><><<<<>>>>

aaaaaad

Posted: **Sat Apr 08, 2017 11:10 pm UTC**

705

<<>><<<>>><<<>><<<>>>>

59.62% efficiency

<<>><<<>>><<<>><<<>>>>

59.62% efficiency

Posted: **Sat Apr 08, 2017 11:47 pm UTC**

706

<><<<><><<<>>>>>

a<<aac>>

<><<<><><<<>>>>>

a<<aac>>

Posted: **Sun Apr 09, 2017 2:01 am UTC**

707

<<><>><<><<><<>>>>

<aa><a<ab>>

spPPpPpPD^{1} or p(PP)p(Pp(Pp(P)))^{1} or spPPpPpPpPpPS^{1}

2112212124

prīmus bisprīmī et prīmus (prīmī et prīmī (prīmī et secundī))

Semiprime (7 * 101)

Asymmetric

Not Alphabetic

Square-free, but recursively only cube-free

Nodes: 9

Reversals: 9

Max Depth: 4

Smoothness: 101

----

^{1}Notes on this version of p-notation I've been developing

**Spoiler:**

<<><>><<><<><<>>>>

<aa><a<ab>>

spPPpPpPD

2112212124

Code: Select all

`*** *****`

* * * ***

* *

*

prīmus bisprīmī et prīmus (prīmī et prīmī (prīmī et secundī))

Semiprime (7 * 101)

Asymmetric

Not Alphabetic

Square-free, but recursively only cube-free

Nodes: 9

Reversals: 9

Max Depth: 4

Smoothness: 101

----

Posted: **Fri Apr 14, 2017 10:56 am UTC**

*sigh* We all want to have 709 don't we?

708

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708

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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.

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709

<<<<<<<>>>>>>>

g (alphabet)

J (SPDFGHIJ/orbitals)

77 (7 up, then 7 down)

septimus

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

----

----

709

<<<<<<<>>>>>>>

g (alphabet)

J (SPDFGHIJ/orbitals)

77 (7 up, then 7 down)

Code: Select all

`*`

*

*

*

*

*

*

septimus

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

----

Posted: **Wed Jun 19, 2019 4:15 pm UTC**

710 = <><<>><<>^{<>}<<>>>

Posted: **Wed Jun 19, 2019 5:22 pm UTC**

711

slurpe

<<>><<>><<><<<<>>>>>

slurpe

<<>><<>><<><<<<>>>>>

Posted: **Thu Jun 20, 2019 9:14 am UTC**

712 = <><><><<<<>>><<<>>>>