600 Terms, a Degree-14 Rational Generating Function, and a Limit Near π

Engineered Operators on Alphabets (EOA) is a research program aimed at creating deterministic recursive operators that map the spoken names of letters into integer sequences. By applying a fixed deterministic operator to the phonetic names of letters, researchers have generated over 600 terms of a single sequence, with the final term containing 249 digits.

The researchers utilized the gfun tool, a Maple package for guessing generating functions from finite sequences, to analyze the data. The gfun tool returned a rational generating function of degree approximately 14, indicating that the sequence satisfies a linear recurrence with constant coefficients. This implies that the sequence extends infinitely, and its limiting ratio of consecutive terms is algebraic.

However, the limit is not exactly equal to π, which is a transcendental number. Instead, the numerical agreement between the limit and π serves as a coincidence. Despite this, the real result lies in the algebraic structure of the degree-13 recurrence that generates the sequence. The generation code is not publicly available, but researchers who are interested in independently verifying and extending the work can request access to the data and generation pipeline upon contacting the researchers.

The data, as well as the generating function, are publicly available, allowing anyone to verify the recurrence. This fascinating result opens several potential avenues for further investigation, including symbolic dynamics, linear recurrences and generating functions, combinatorics on words, coding theory and compression, cryptography and pseudorandom generation, machine learning and representation learning, and mathematical linguistics.