The Alphabet as a Sequence Engine: A Census of What Letter Names Generate, and What the OEIS Has Never Seen
Abstract 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…,…
This census investigates the integer sequences produced by 36 human writing systems using a fixed recursive expansion rule applied to each letter's name. Across 1,056 resulting sequences, three key facts emerge:
First, the growth rates of these sequences align closely with a small set of algebraic numbers: 2.618..., 3.414..., 2.414..., 2, and 3, with 2.618... (the square of the golden ratio, φ²) appearing most frequently.
Second, several of the generated sequences correspond directly to well-known mathematical series, including the powers of two, Fibonacci bisections, Lucas bisections, Pell numbers, Mersenne numbers, and the series of counting numbers.
Third, 388 distinct sequences generated by the scripts do not appear in the On-Line Encyclopedia of Integer Sequences (OEIS), suggesting these patterns may be unique. Two random baseline controls tested to confirm the rarity of these findings were: random alphabets of matched size never produce the core patterns found in natural scripts (0 of 250 simulations), and the English E5 alphabet splits into two equal halves, a pattern not seen in random alphabets (0 of 100 simulations).
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