Riffs and Rotes • Happy New Year 2025
• https://inquiryintoinquiry.com/2025/01/01/riffs-and-rotes-happy-new-year-2025/

$\text{Let}{p}_n=\text{the}{n}^{\text{th}}\text{prime}.$

$\text{Then}2025=81\cdot 25=3^4{5}^2$

$={p_2}^4{p_3}^2={p_2}^{{p_1}^{p_1}}{p_3}^{p_1}={p_{p_1}}^{{p_1}^{p_1}}{p_{p_2}}^{p_1}={p_{p_1}}^{{p_1}^{p_1}}{p_{p_{p_1}}}^{p_1}$

No information is lost by dropping the terminal 1s. Thus we may write the following form.

$$2025={p_p}^{p^p}{p_{p_p}}^p$$

The article linked below tells how forms of that sort correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”. The riff and rote for 2025 are shown in the next two Figures.

Riff 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/riff-2025.png

Rote 2025
• https://inquiryintoinquiry.files.wordpress.com/2025/01/rote-2025.png

Reference —

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

#Arithmetic #Combinatorics #Computation #Factorization #GraphTheory #GroupTheory
#Logic #Mathematics #NumberTheory #Primes #Recursion #Representation #RiffsAndRotes

Riffs and Rotes • Happy New Year 2025

No information is lost by dropping the terminal 1s.  Thus we may write the following form.

The article linked below tells how forms of that sort correspond to a family of digraphs called riffs and a family of graphs called rotes.  The riff and rote for are shown in the next two Figures.

Riff 2025

Rote 2025

Reference

• Riffs and Rotes

cc: Academia.edu • Cybernetics • Structural Modeling • Systems Science
cc: Conceptual Graphs • Laws of Form • Mathstodon • Research Gate

Riffs and Rotes • Happy New Year 2024
• https://inquiryintoinquiry.com/2024/01/02/riffs-and-rotes-happy-new-year-2024/

$\text{Let}{p}_n=\text{the}{n}^{\text{th}}\text{prime}.$

$\text{Then}2024=8\cdot 11\cdot 23=p_1^3{p}_5{p}_9=p_1^{p_2}{p}_{p_3}{p}_{p_2^2}=p_1^{p_{p_1}}{p}_{p_{p_2}}{p}_{p_{p_1}^{p_1}}=p_1^{p_{p_1}}{p}_{p_{p_{p_1}}}{p}_{p_{p_1}^{p_1}}$

No information is lost by dropping the terminal 1s. Thus we may write the following form.

$$2024=p^{p_p}\cdot p_{p_{p_p}}\cdot p_{p_p^p}$$

The article referenced below tells how forms like these correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”.

The riff and rote for 2024 are shown in the next two Figures.

Riff 2024
• https://inquiryintoinquiry.files.wordpress.com/2024/01/riff-2024.png

Rote 2024
• https://inquiryintoinquiry.files.wordpress.com/2024/01/rote-2024.png

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

#TodaysAcronym ☞ #DIYFFAN

#DoItYourselfFunFactoidsAboutNumbers

#RiffsAndRotes
• https://oeis.org/wiki/Riffs_and_Rotes

Riffs and Rotes • Happy New Year 2023
• https://inquiryintoinquiry.com/2023/01/01/riffs-and-rotes-happy-new-year-2023/

$\text{Let}{p}_n=\text{the}{n}^{\text{th}}\text{prime}.$

$\text{Then}2023=7\cdot {17}^2=p_4{p}_7^2=p_{{p_1}^{p_1}}{p}_{p_4}^{p_1}=p_{{p_1}^{p_1}}{p}_{p_{{p_1}^{p_1}}}^{p_1}$

No information is lost by dropping the terminal 1s. Thus we may write the following form.

$$2023=p_{p^p}{p}_{p_{p^p}}^p$$

Forms like these correspond to a family of #Digraphs called #Riffs and a family of #Graphs called #Rotes.

#RiffsAndRotes • Happy New Year 2023
• https://inquiryintoinquiry.com/2023/01/01/riffs-and-rotes-happy-new-year-2023/

$2023=7\cdot {17}^2=p_4{p}_7^2=p_{p_1^{p_1}}{p}_{p_4}^{p_1}=p_{p_1^{p_1}}{p}_{p_{p_1^{p_1}}}^{p_1}$

Happy New Year

$2023=p_4^1{p}_7^2=p_{p_1^2}{p}_{p_4^1}^2$

#RiffsAndRotes
• https://oeis.org/wiki/Riffs_and_Rotes

Just experimenting a little —
will add more explanation later —

#RiffsAndRotes
• https://oeis.org/wiki/Riffs_and_Rotes

#Riffs from 1 to 60
• https://oeis.org/w/images/1/17/Animation_Riff_60_x_0.16.gif

#Rotes from 1 to 60
• https://oeis.org/w/images/e/ee/Animation_Rote_60_x_0.16.gif

#Arithmetization #GödelNumbering
#DoublyRecursiveFactorization #DRF
#Arithmetic #GraphTheory #NumberTheory
#Primes #PrimeNumbers #PrimesFactorization

#RiffsAndRotes
• https://oeis.org/wiki/Riffs_and_Rotes

#Arithmetization #GödelNumbering
#DoublyRecursiveFactorization #DRF
#Arithmetic #NumberTheory #GraphTheory
#PrimesFactorization #PrimeNumbers #Primes

Riffs and Rotes
• https://oeis.org/wiki/Riffs_and_Rotes

#RiffsAndRotes #Primes
#Arithmetic #Arithmetization
#GraphTheory #NumberTheory
#PrimeNumbers #GödelNumbers