[seqfan] Riffs and Rotes • Happy New Year 2023

[Jon Awbrey]

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

SeqFans,

Let pₙ = the n-th prime.

Then 2023
= 7∙17²
= p₄∙p₇²
= p_{p₁^p₁} ∙ {p_{p₄}}^{p₁}
= p_{p₁^p₁} ∙ {p_{p_{p₁^p₁}}}^{p₁}

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 those correspond to a family of digraphs
called riffs and a family of graphs called rotes,
as described in the following OEIS Wiki article.

Riffs and Rotes ( https://oeis.org/wiki/Riffs_and_Rotes )

The riff and rote for 2023 are shown in the next two Figures.

Riff 2023
https://oeis.org/w/images/c/cc/Riff_2023_Big.jpg

Rote 2023
https://oeis.org/w/images/8/8d/Rote_2023_Big.jpg

Regards,

Jon