The Alphabet as a Sequence Engine: A Census of What Letter Names Generate, and What the OEIS Has Never Seen

We evaluate the integer sequences generated across 36 human writing systems under the Engineering of Alphabets (EOA) operator. Auditing all 1,056 resulting sequences against the On-Line Encyclopedia of Integer Sequences (OEIS), three facts survive every check we could devise. First, the growth rates of these sequences cluster on a small set of exact algebraic numbers 2.618…, 3.414…, 2.414…, 2, and 3, with 2.618… (φ²) the single largest cluster. Second, several of the generated sequences are, term for term, classics of mathematics: the powers of two, the Fibonacci bisections, the Lucas bisection, the Pell family, the Mersenne numbers, and the bare counting numbers, each verified against the full published OEIS record (up to 90 terms) from our 500-term exact sequences. Third, 388 distinct generated sequences appear in no catalogue, although every one satisfies an explicit integer linear recurrence. To test whether these observations arise by chance, we evaluate two random-baseline controls: random alphabets of matched size never form the tiny cores that natural scripts form (0 of 250 simulations), and the English E5 spectrum splits into two equal halves, a pattern random alphabets never produce (0 of 100 simulations). We release the full census, the matrices, and the verification code, and we pose two challenges to the sequence community.