Length 200 over {0, 1, 2, 8} — Additive Squares

Word of length 200 over {0, 1, 2, 8}

by Aayush Rajasekaran, 2026-08-31 · the current record for this alphabet · JSON

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

1 0 1 8 0 2 0 1 2 1 8 2 1 2 0 8 0 2 0 1 0 2 0 8 2 8 1 8 2 0 8 0 1 8 0 8 2 8 1 8 2 8 0 2 1 2 0 2 8 0 8 1 8 0 2 1 0 1 8 1 0 2 1 2 8 2 1 2 0 2 8 1 0 1 2 0 1 0 8 0 1 0 2 0 8 2 1 2 8 2 0 8 0 1 8 0 8 2 8 1 2 8 2 0 2 1 0 2 0 8 1 8 2 8 0 2 0 1 0 8 0 2 8 0 8 1 8 0 8 2 8 1 2 8 2 0 8 1 8 0 8 2 0 1 0 2 8 2 1 8 2 8 0 2 1 2 8 0 2 0 1 0 2 0 8 0 2 1 2 8 0 8 1 0 8 0 2 8 1 8 0 2 8 2 1 2 0 2 8 0 8 1 0 8 0 2 1 0 2 8

Alphabet {0, 1, 2, 8}

size 4 · diameter 8 · record length 200 · 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

200 (was 179) — Aayush Rajasekaran, 2026-08-31
179 (was 178) — Aayush Rajasekaran, 2026-08-26
178 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-31 00:40 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 201 exists over this alphabet, so max = 200. Closure claim to follow.

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