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In a now-deleted comment, Consigliere ZARF listed a number of papers published in Zeitschrift für Physik in the late 1920's that used this notation. The earliest was Pascual Jordan's 1927 "Über eine neue Begründung der Quantenmechanik", using the notation on pp.816-817; with about 10 other papers published in the following few years, all in the ZfP, all ...

3

On Bibliography of Quaternions and Allied Mathematics by Alexander Macfarlane I found this: On page 72; James Byrnie Shaw 1896 Sedenions (title). American Assoc. Proc., 45, 26. I couldn't find this reference, but the same author wrote this book: Synopsis of Linear Associative Algebra: A Report on its Natural Development and Results Reached up to the ...

6

There are (at least) two different types of numbers called "sedenions". The first ones were introduced by Muses in 1980, who called them $16$-ions, and renamed into "sedenions" by Carmody in 1988. However, Sorgsepp and Lohmus beat him to the name in Binary and Ternary Sedenions (1981), which they used more in line with "quaternions" and "octonions" (sedecim ...

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