Length 139 over {0, 2, 3, 7} — Additive Squares

Word of length 139 over {0, 2, 3, 7}

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

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

7 2 7 0 2 0 3 2 7 3 7 0 7 2 7 3 7 0 3 0 2 3 2 7 2 0 7 2 7 3 0 7 0 2 0 3 0 2 0 7 2 0 2 3 2 0 2 7 2 3 7 0 7 2 0 7 0 3 0 2 3 2 7 2 0 7 3 7 2 3 7 3 0 3 2 3 7 2 7 0 7 2 7 3 7 0 3 7 3 2 3 7 3 0 3 2 0 7 2 7 3 7 2 0 7 0 3 0 2 3 2 7 2 0 2 3 0 2 0 7 0 2 0 3 2 3 7 2 7 0 7 3 2 3 7 3 0 3 7

Alphabet {0, 2, 3, 7}

size 4 · diameter 7 · record length 139 · 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

139 (was 137) — Aayush Rajasekaran, 2026-08-30
137 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-30 19:40 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 140 exists over this alphabet, so max = 139. Closure claim to follow.

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