Length 113 over {0, 2, 3, 6} — Additive Squares

Word of length 113 over {0, 2, 3, 6}

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

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

6 3 6 0 6 3 6 2 6 0 3 2 0 6 0 3 2 3 6 0 3 2 6 2 0 6 2 6 3 6 2 6 0 6 3 0 3 2 6 0 6 3 6 2 0 2 6 2 0 3 0 6 0 2 3 6 3 0 6 0 2 0 3 0 2 0 6 2 0 2 3 2 6 3 0 6 3 2 6 0 2 0 3 0 6 0 2 6 0 6 3 6 2 6 3 6 0 3 2 6 2 0 6 2 6 3 0 2 3 6 2 3 0

Alphabet {0, 2, 3, 6}

size 4 · diameter 6 · record length 113 · 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

113 (was 112) — Aayush Rajasekaran, 2026-08-30
112 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-30 18:34 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 114 exists over this alphabet, so max = 113. Closure claim to follow.

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