Length 171 over {0, 3, 4, 8} — Additive Squares

Word of length 171 over {0, 3, 4, 8}

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

Display: drawn for the equivalent alphabet translated by -4 (drift removed).

0 8 4 0 3 8 4 3 8 3 0 4 8 0 3 8 0 8 4 8 0 8 3 8 4 3 8 3 0 3 8 3 4 8 4 0 3 8 0 3 0 4 0 3 8 0 8 4 8 0 8 3 8 4 3 0 3 8 0 3 0 4 3 8 4 0 8 0 3 0 4 0 3 0 8 3 0 3 4 3 0 3 8 3 4 8 4 0 8 3 0 3 4 0 3 0 8 0 4 8 0 8 3 8 4 8 3 8 0 3 0 4 3 0 3 8 3 4 8 3 8 0 8 3 8 4 8 0 4 8 4 3 8 3 0 3 8 4 8 3 8 0 3 0 4 0 3 0 8 0 4 8 0 8 3 0 4 0 3 0 8 3 8 4 3 8 3 0 8 3 8

Alphabet {0, 3, 4, 8}

size 4 · diameter 8 · record length 171 · 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

171 (was 165) — Aayush Rajasekaran, 2026-08-30
165 (was 164) — Aayush Rajasekaran, 2026-08-26
164 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-30 19:15 UTC

This word attains the exact maximum: our 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 172 exists over this alphabet, so max = 171. Closure claim to follow.

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