Additive Squares

Word of length 6796 over {0, 1, 2, 11, 17, 19}

by David Renshaw, 2026-10-05 · the current record for this alphabet · JSON

Display: drawn for the equivalent alphabet translated by -8 (drift removed); downsampled ×6.

17 2 11 19 2 17 2 1 0 17 11 0 1 2 0 2 19 0 11 17 11 1 17 2 11 17 11 0 2 0 17 19 11 2 19 1 17 19 11 0 17 19 17 2 0 2 17 19 1 17 11 19 2 17 11 2 0 11 17 1 0 19 17 11 2 0 2 1 0 19 11 2 19 17 0 1 11 19 2 1 19 11 17 1 11 19 0 1 17 19 1 11 17 19 11 0 19 11 1 17 19 1 0 19 11 1 17 19 17 0 1 17 19 11 17 11 0 19 11 0 2 1 19 17 11 0 2 0 19 17 0 2 11 17 1 19 11 2 19 0 11 19 17 2 1 11 19 17 0 17 1 19 1 17 1 2 19 2 1 0 19 1 11 0 17 0 2 17 11 1 2 11 0 2 17 11 0 1 17 0 11 19 17 2 1 11 19 2 1 19 17 0 11 2 11 17 1 0 1 2 11 0 2 19 0 1 0 2 11 17 1 0 11 1 2 19 2 17 11 0 17 19 1 2 0 17 1 11 0 19 1 2 0 19 17 0 2 17 11 0 17 19 2 0 11 2 11 1 17 11 19 17 2 19 17 0 19 0 11 17 1 19 0 1 2 0 11 19 1 2 19 17 11 19 2 11 1 0 11 1 2 11 2 19 2 1 19 17 2 1 0 2 17 0 11 2 17 2 0 17 2 19 2 0 17 1 19 11 17 19 17 0 19 0 2 11 0 19 2 19 17 0 2 19 1 19 11 1 11 2 17 0 17 2 17 11 2 17 1 19 11 19 2 19 0 19 1 19 17 11 19 1 2 17 19 2 0 17 1 2 17 19 2 1 17 11 1 19 17 1 11 2 19 11 17 11 1 11 2 1 0 17 1 0 11 1 17 19 2 17 1 11 0 1 17 19 11 0 11 17 0 17 19 11 0 17 1 19 11 0 19 2 19 1 0 11 17 11 1 17 11 0 2 11 17 19 1 11 17 0 2 1 2 0 2 11 2 19 0 11 2 19 17 11 0 2 11 0 17 11 1 19 0 17 0 11 2 11 17 19 17 2 11 1 19 0 19 17 11 2 0 17 11 1 17 0 1 17 11 1 2 11 17 1 0 17 11 19 0 1 2 19 11 1 19 0 19 17 0 11 2 0 11 1 19 2 0 1 2 11 1 0 19 17 0 2 1 19 2 0 11 1 0 11 17 1 2 1 11 17 19 11 2 17 1 2 11 19 2 1 19 1 0 2 1 19 17 0 2 11 2 19 2 1 11 17 19 17 2 19 1 17 11 19 2 1 19 0 17 11 19 17 19 0 19 2 19 0 11 19 17 0 19 1 11 0 1 17 11 1 2 19 1 19 11 17 1 19 11 0 1 19 1 0 17 0 1 19 2 0 1 17 1 19 2 11 2 17 1 11 0 17 11 0 2 0 1 2 0 17 1 2 17 1 19 2 17 1 0 17 0 19 1 11 0 1 2 0 11 2 0 19 11 2 19 17 11 1 17 19 2 0 19 1 17 0 19 11 17 1 11 1 19 11 2 17 0 17 19 17 0 2 11 0 1 17 2 19 17 1 0 19 1 2 19 0 19 11 2 0 19 1 19 2 0 2 19 2 1 2 11 19 11 2 11 0 2 0 1 11 0 2 0 19 2 11 17 11 2 0 11 1 2 1 17 2 0 1 2 0 11 2 0 19 11 2 0 11 17 0 11 1 11 17 11 2 11 1 2 0 19 11 1 0 11 19 11 1 0 17 2 17 1 19 2 0 19 11 1 2 0 11 2 19 11 1 17 11 19 2 11 0 2 17 11 19 1 2 0 17 0 11 1 0 17 2 1 0 2 19 17 11 17 0 2 17 11 1 19 0 1 17 0 1 2 0 11 1 2 11 1 11 0 17 0 19 11 1 11 2 0 19 1 11 2 0 1 2 1 11 17 0 11 2 0 11 17 0 17 19 2 11 17 19 17 0 1 17 19 11 17 11 1 11 17 2 0 2 11 19 17 11 0 19 2 1 17 1 11 17 2 17 19 2 0 1 17 0 2 17 11 19 1 11 1 0 2 1 11 19 17 2 0 1 0 19 17 0 2 17 11 19 2 19 17 0 19 11 2 11 19 17 11 0 19 0 17 1 0 2 19 1 17 0 1 2 11 19 0 2 0 11 17 0 11 2 1 2 19 11 17 1 17 19 11 19 1 11 19 0 2 11 19 17 0 19 2 11 2 0 17 2 17 19 11 1 19 17 11 2 19 17 11 17 0 19 11 2 19 17 11 1 17 11 19 2 11 0 17 11 2 11 19 2 0 17 2 19 1 2 0 11 17 1 17 2 1 17 11 0 11 1 11 19 0 19 11 17 0 19 0 11 2 19 1 2 0 1 11 0 2 0 19 11 19 2 0 2 19 11 1 2 11 19 17 19 0 2 11 1 19 17 11 19 2 1 19 2 11 2 0 1 2 11 17 0 11 17 2 17 0 17 11 17 1 2 11 17 19 11 2 19 0 2 19 11 17 11 19 1 0 11 0 1 0 19 1 11 19 11 17 19 17 0 19 11 17 1 19 1 11 1 19 17 19 11 19 17 2 11 2 0 17 2 19 11 19 2 19 1 19 11 17 19 2 19 17 19 11 17 19 0 11 2 19 11 1 19 17 0 17 11 19 17 0 2 19 11 19 17 2 1 0 11 19 0 1 2 0 19 2 0 17 19 0 19 11 1 19 0 19 1 2 19 0 17 0 2 17 0 1 2 0 11 2 19 0 1 17 0 17 11 19 17 1 17 2 1 2 11 0 2 19 2 1 19 2 17 11 1 17 19 11 19 0 19 11 19 2 11 1 19 0 11 19 2 0 17 11 2 19 17 11 2 1 11 19 2 1 2 0 17 2 11 0 1 19 2 19 17 19 1 17 0 1 2 0 2 19 2 1 0 2 11 19 0 11 17 19 0 2 19 11 1 19 17 2 11 19 1 11 1 0 1 17 0 2 0 1 11 1 2 19 1 11 17 2 1 0 2 11 17 11 2 19 17 11 0 17 11 1 0 1 2 11 2 0 2 17 1 2 11 2 19 2 1 17 11 1 2 11 2 0 1 2 17 11 1 0 2 19 11 1 11 2 17 19 1 19 11 19 2 19 11 19 17 1 17 0 11 1 11 19 1 0 17 19 2 11 19 1 19 2 1 2 0 1 11 2 19 1 11 0 17 19 17 11 2 11 19 2 1 2 19 17 2 11 17 0 17 19 2 11 17 19 17 1 2 11 1 2 19 0 1 2 11 2 0 2 1 0 1 17 11 2 0 2 1 0 2 19 1 19 11 2 19 0 17 19 2 17 19 1 17 19 0 11 2 0 11 1 19 2 19 11 2 17 2 19 17 19 1 17 11 2 0 11 2 19 0 19 17 19 11 17 1 19 2 19 11 19 17 11 2 19 17 1 11 17 0 17 19 11 17 11 1 11 2 0 2 17 19 1 2 11 17 2 19 17 0 17 19 1 2 0 1 17 2 11 1 2 0 19 1 19 17 2 1 0 2 17 1 19 17 0 19 11 17 19 2 11 0 1 17 0 2 19 2 1 11 0 19 0 1 19 17 11 19 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0 19 0 2 1 11 2 0 17 1 17 19 0 2 0 19 11 19 17 11 19 0 11 1 19 0 19 17 19 11 2 0 17 11 17 1 17 0 19 1 2 19 17 11 0 19 1 2 11 0 19 0 1 0 19 0 11 0 2 11 2 17 1 19 11 17 19 11 19 1 2 19 11 17 11 1 19 0 1 2 11 19 1 11 19 11 0 19 11 2 0 19 17 19 11 17 19 2 1 11 2 17 11 19 11 2 19 0 11 2 11 1 0 19 11 17 1 17 2 0 17 19 11 17 2 19 17 19 0 1 0 2 19 17 19 0 2 11 19 1 19 17 19 2 17 11 0 19 2 11 0 2 0 1 2 0 17 0 11 2 11 19 17 11 2 19 2 11 0 2 11 17 0 1 11 19 1 2 17 19 2 19 11 1 17 0 19 11 19 2 17 2 1 2 17 0 2 0 1 2 19 17 1 2 0 11 2 19 0 2 0 17 2 17 11 2 0 11 2 1 2 0 1 17 2 1 0 11 1 17 0 19 11 19 2 1 2 17 2 1 0 17 19 17 1 0 2 11 17 1 0 19 2 0 11 1 2 0 1 2 19 0 2 1 0 17 0 2 11 1 19 0 1 19 11 1 19 2 19 1 11 19 17 11 1 19 0 17 11 0 2 11 19 1 19 2 11 17 19 11 2 11 1 11 0 1 19 17 11 1 0 2 11 17 11 0 1 2 0 2 11 19 1 2 11 17 1 0 1 19 2 11 17 11 2 11 1 19 2 1 2 11 0 1 11 19 0 1 17 1 19 17 19 0 19 2 19 11 0 17 2 17 19 2 0 2 1 2 0 2 19 11 1 2 11 17 11 1 11 19 2 0 2 1 11 2 1 17 19 1 17 0 2 1 0 1 11 0 2 17 0 1 11 0 1 2 11 2 1 19 0 2 11 0 11 19 11 2 0 17 0 11 1 0 2 0 17 11 0 1 11 2 0 1 2 1 19 11 0 1 0 2 1 0 17 0 11 1 11 2 17 0 11 1 17 19 2 19 17 11 17 0 19 0 2 19 17 0 1 17 2 1 0 11 2 0 2 19 0 1 2 1 11 2 1 0 19 2 19 1 2 17 11 17 19 1 0 1 17 11 2 0 1 17 1 2 1 0 2 1 19 1 0 19 1 11 1 0 2 1 0 17 1 0 11 1 2 11 17 0 2 19 1 2 11 19 11 1 19 0 11 1 0 2 1 19 0 2 1 0 2 0 19 11 1 11 2 1 2 0 1 11 1 17 19 2 1 19 11 2 0 11 19 17 1 17 2 1 19 2 17 0 1 2 19 2 0 2 11 2 1 0 17 0 2 0 1 19 2 1 2 11 1 0 19 11 0 1 2 0 1 17 0 2 0 1 0 2 11 0 2 1 2 17 2 1 0 11 0 2 1 0 2 11 17 19 2 1 0 2 17 11 1 0 11 19 17 19 2 1 0 17 2 19 2 0 1 2 0 11 1 17 0 1 19 2 0 17 1 0 19 2 19 0 19 17 19 11 1 17 19 1 2 0 17 2 19 17 1 2 17 19 11 19 2 1 2 11 17 2 0 2 11 1 17 0 17 2 1 0 2 19 0 11 19 2 19 0 1 19 2 17 0 1 0 11 19 17 1 19 11 19 2 0 19 1 17 2 0 1 0 19 11 19 0 19 11 2 11 1 2 0 1 2 17 1 0 1 2 19 11 1 2 0 17 2 19 2 0 2 11 19 2 0 11 0 2 1 0 17 1 2 11 19 1 19 0 1 17 11 19 17 11 2 0 1 19 2 0 17 19 2 1 19 11 1 0 17 0 1 19 1 0 17 11 1 11 2 0 2 17 2 1 0 2 11 1 0 2 0 17 0 2 19 0 2 1 2 11 19 1 11 0 2 1 19 2 17 0 2 0 11 2 1 2 0 2 19 11 2 11 1 19 11 1 0 2 19 17 2 0 17 2 1 2 11 0 11 1 19 1 2 19 11 2 11 0 11 1 2 1 0 19 1 2 1 0 1 11 2 11 17 0 2 19 0 2 1 0 2 0 11 17 2 0 1 19 17 0 2 19 2 11 2 1 2 0 1 11 1 0 2 1 17 1 2 0 2 11 1 2 1 0 2 19 2 1 17 0 2 19 2 11 2 1 2 19 2 0 11 0 17 11 19 2 19 0 2 0 1 2 1 11 1 0 2 19 11 2 0 11 1 2 11 0 2 0 17 11 1 17 0 19 1 2 11 2 1 0 17 0 2 0 11 17 2 0 17 19 0 11 19 17 11 17 1 11 2 1 11 17 1 0 11 1 17 2 1 11 19 11 1 17 0 2 11 0 11 1 17 19 11 0 11 19 2 0 1 19 17 19 0 1 11 2 17 0 2 0 19 1 17 11 19 11 17 0 17 19 17 1 17 2 11 17 1 17 0 1 0 11 17 19 11 2 17 19 11 19 1 0 17 11 19 17 11 1 2 19 11 2 0 2 19 1 2 0 2 17 2 0 1 11 17 11 19 1 0 19 11 0 19 2 19 1 0 2 19 17 19 0 2 1 2 17 11 0 17 2 17 19 1 17 2 11 0 1 0 2 0 11 2 1 17 11 0 11 1 2 0 1 11 19 1 2 19 1 17 0 2 17 11 2 1 11 0 17 0 2 0 1 11 0 2 19 11 2 0 1 17 19 2 0 1 2 11 19 2 1 19 17 2 1 11 17 11 2 11 19 17 19 0 1 17 0 17 19 0 19 1 2 19 1 11 2 19 11 17 2 1 17 19 17 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17

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Alphabet {0, 1, 2, 11, 17, 19}

size 6 · diameter 19 · record length 6796 · 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

• 6796 (was 224) — David Renshaw, 2026-10-05
• 224 (first) — Bryna Kra, 2026-08-26

Comments

• David Renshaw · 2026-10-05 14:28 UTC

  Found by beam search over prefixes scored by randomized DFS rollouts (from scratch, ~2 min), then iterated cut-and-re-extend local search on both ends (~7 min, 10 cores).

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