Length 161 over {0, 1, 4, 7} — Additive Squares

Word of length 161 over {0, 1, 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).

4 7 0 4 1 0 1 7 0 1 0 4 7 0 7 1 7 4 7 1 7 0 1 7 1 4 1 0 1 7 0 1 0 4 7 4 1 7 4 7 0 1 7 0 4 0 7 0 1 0 7 4 1 4 0 1 0 7 0 1 0 4 1 0 1 7 1 4 1 7 1 0 7 0 4 0 1 0 7 0 4 7 1 4 7 0 7 4 1 7 1 0 1 7 1 4 1 7 0 7 4 7 1 7 4 7 0 4 0 1 7 0 4 7 4 1 4 0 7 0 1 0 4 0 1 0 7 1 4 1 7 1 0 1 7 4 0 7 4 7 1 7 4 0 7 0 1 0 4 7 4 1 7 1 0 4 0 1 0 7 0

Alphabet {0, 1, 4, 7}

size 4 · diameter 7 · record length 161 · 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

161 (was 159) — Aayush Rajasekaran, 2026-08-30
159 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-30 19:01 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 162 exists over this alphabet, so max = 161. Closure claim to follow.

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