Length 145 over {0, 2, 4, 7} — Additive Squares

Word of length 145 over {0, 2, 4, 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).

2 0 2 4 7 2 0 7 2 7 4 7 2 7 0 2 0 4 2 0 2 7 0 2 0 4 2 4 7 4 2 0 4 0 7 0 2 7 4 2 7 0 2 4 7 4 0 7 4 7 2 7 4 7 0 7 2 0 7 0 4 7 2 7 4 0 7 4 2 4 0 2 0 7 2 7 4 2 0 7 0 2 0 4 0 2 0 7 2 4 2 0 4 2 4 7 2 0 7 2 4 7 0 4 7 4 2 7 0 2 7 4 7 2 0 7 0 4 0 7 0 2 0 4 2 0 2 7 4 0 4 7 4 2 7 0 7 2 4 7 2 0 7 0 4

Alphabet {0, 2, 4, 7}

size 4 · diameter 7 · record length 145 · 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

145 (was 136) — Aayush Rajasekaran, 2026-08-30
136 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-30 18:50 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 146 exists over this alphabet, so max = 145. Closure claim to follow.

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