Length 215 over {0, 1, 4, 8} — Additive Squares

Word of length 215 over {0, 1, 4, 8}

by Aayush Rajasekaran, 2026-08-31 · the current record for this alphabet · JSON

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

0 8 4 0 8 0 1 8 0 8 4 1 8 1 0 1 8 1 4 1 0 4 8 0 8 1 8 4 0 4 8 4 1 0 8 0 1 0 4 0 1 0 8 1 4 1 0 8 1 8 4 8 0 4 0 1 0 8 1 0 1 4 1 8 1 0 8 1 8 4 8 1 8 0 1 0 4 8 1 8 4 8 0 8 4 8 1 4 0 4 8 0 4 0 1 4 1 8 4 8 0 8 4 1 8 1 0 1 4 1 0 1 8 0 1 0 4 8 1 4 8 4 0 8 0 1 0 4 0 1 0 8 1 0 1 4 8 4 0 1 0 8 1 0 1 4 1 0 1 8 1 4 8 1 8 0 4 0 1 8 0 8 4 8 1 8 4 8 0 4 8 1 4 0 8 0 4 0 1 8 1 4 0 4 8 1 8 0 1 8 1 4 1 0 1 8 0 1 0 4 0 1 0 8 0 4 8 1 4 1 0 1 4 1 8

Alphabet {0, 1, 4, 8}

size 4 · diameter 8 · record length 215 · 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

215 (was 205) — Aayush Rajasekaran, 2026-08-31
205 (was 195) — Aayush Rajasekaran, 2026-08-30
195 (was 194) — Aayush Rajasekaran, 2026-08-26
194 (first) — Aayush Rajasekaran, 2026-08-20

Comments

Aayush Rajasekaran · 2026-08-31 01:33 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 216 exists over this alphabet, so max = 215. Closure claim to follow.

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