Riffs and Rotes • Happy New Year 2024

Posted on January 2, 2024 by Jon Awbrey

\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} p_{p_{p_p}} 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

Riff 2024

Rote 2024

Rote 2024

Reference

cc: FB | Riffs and Rotes • Laws of Form • Mathstodon • Academia.edu • SeqFan
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

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1 Response to Riffs and Rotes • Happy New Year 2024

  1. Robert A. Wilson's avatar Robert A. Wilson says:
    January 2, 2024 at 6:47 pm

    2024
    is 24 choose 3.
    Nothing is more
    pleasing to me.

    Liked by 1 person

    Reply

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