Additive Squares

Word of length 141 over {0, 1, 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).

1 7 1 0 7 0 3 7 0 7 1 0 7 0 3 7 3 1 7 0 7 3 0 7 0 1 0 3 1 0 1 7 3 0 7 0 1 7 1 3 1 7 1 0 7 1 7 3 7 0 7 3 7 1 3 0 7 3 1 7 1 0 1 7 3 1 3 0 1 3 7 0 1 7 0 7 3 1 3 7 0 3 0 1 0 7 0 1 0 3 1 0 1 7 1 3 1 0 3 1 3 7 3 1 3 0 1 0 7 1 7 3 7 1 7 0 7 3 0 7 0 1 7 1 3 0 1 0 7 0 3 0 7 0 1 7 0 7 3 7 1

← previous record (139)

Alphabet {0, 1, 3, 7}

size 4 · diameter 7 · record length 141 · JSON

closed The exact maximum additive-square-free word length over this alphabet is 141. exhaustive search

Closure claims

• accepted max 141 claimed by David Renshaw, 2026-10-05 · evidence — exhaustive search

Record history

• 141 (was 139) — Aayush Rajasekaran, 2026-08-30
• 139 (was 106) — Aayush Rajasekaran, 2026-08-20
• 106 (first) — David Renshaw, 2026-08-18

Comments

• Aayush Rajasekaran · 2026-08-30 18:49 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 142 exists over this alphabet, so max = 141. Closure claim to follow.

Log in to comment.

← all record words