User:J. Conrad

Sociomathematician (colloquialist) at Complexor.

• My website
• See my contributions to the OEIS
• GitHub
• r/OEIS on Reddit

Signature Left Near-Ring (SNR)

I wrote a couple papers exploring a variation of the INVERT transform which I have termed the Signature Left Near-Ring. It includes methods for computing many unique sequences, as well as a more enthusiastic treatment of a somewhat neglected subject to the OEIS.

• Recursive Signatures and the Signature Left Near-Ring - I lay out the parameters for SNR and explore its consequences.
• The Signature Function and Higher-Dimensional Objects - I define and explore "canonical" signature-bearing objects as generalized to an arbitrary number of dimensions; through this process I discovered an algorithm which reduces an apparently-exponential computation down to O(n^3).
• More on the Signature Function The latest installment on signature arithmetic, I explore various identities, unique sequences and signatures, base interpretations of matrices and prisms, and miscellaneous identities. I also introduce a set of conjectures and open problems relating to signatures.

I am currently working on a part 4, which specifically explores a particular representation of Cantor's diagonal argument, its matrix representation, and the resultant identities.

Choix de Bruxelles/Brussels Choice (CDB)

Lately I have worked on Choix de Bruxelles. My first published sequence, A356511, is the base-12 analogue to A323289 and contained 16 terms. Shortly after I created A356715 for ternary. Shoutout to Michael S. Branicky for computing additional terms for both sequences and providing independent verification through the process.

• Choix de Bruxelles (Python)
• base64.py, used for arbitrary-base arithmetic

Sociomathematics

I like to write about topics of interest in a way that is accessible to a younger and/or less-experienced audience. I'm particularly proud of Hypernumbers, a topic which I feel is easy to grok and even easier to see exhibited in the wider social world.

• Positional Numeral Systems with Sequences as the Base - Academically referred to as Mu representations, but with more hands-on approach to explaining positional numeral systems
• Hypernumbers - Hidden in Plain Sight - If you interface with IP addresses, then you've already been working with Hypernumbers. I highly recommend it, as it might open your eyes to something truly fascinating