Length 184 over {0, 2, 3, 8} — Additive Squares

Word of length 184 over {0, 2, 3, 8}

by Aayush Rajasekaran, 2026-08-30 · the current record for this alphabet · JSON

Display: drawn for the equivalent alphabet translated by -3 (drift removed).

0 2 3 0 3 8 0 2 8 3 8 0 3 0 2 3 0 3 8 3 2 8 2 0 8 2 8 3 8 0 3 8 3 2 8 0 2 3 0 2 0 8 0 2 0 3 0 8 3 8 2 3 8 0 3 0 2 3 8 2 8 0 8 2 3 8 3 0 8 3 8 2 8 0 8 2 8 3 2 8 0 2 0 3 2 8 3 8 0 8 2 8 3 8 0 3 0 2 3 8 3 2 0 3 2 8 2 0 2 3 0 3 8 2 3 0 2 0 8 0 3 0 2 3 0 3 8 3 2 8 3 8 0 2 3 0 8 0 2 3 2 8 0 8 2 3 8 3 0 8 3 8 2 8 0 8 2 8 3 2 0 8 0 2 0 3 2 0 8 3 2 8 3 8 0 3 0 2 3 8 0 3 2 3

Alphabet {0, 2, 3, 8}

size 4 · diameter 8 · record length 184 · JSON

open No exhaustive search has settled this alphabet; the record is a lower bound on the (possibly infinite) maximum.

Know the exact maximum? Log in to claim this alphabet closed.

Record history

184 (was 160) — Aayush Rajasekaran, 2026-08-30
160 (was 159) — Aayush Rajasekaran, 2026-08-26
159 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-30 23:36 UTC

This word attains the exact maximum: exhaustive search (Rust backtracking engine over prefix sums; counts cross-validated against a naive implementation and against this site's closed alphabets) proves no additive-square-free word of length 185 exists over this alphabet, so max = 184. Closure claim to follow.

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