Length 575 over {0, 1, 2, 3, 4, 7}

Word of length 575 over {0, 1, 2, 3, 4, 7}

by David Renshaw, 2026-08-19 · the current record for this alphabet · JSON

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

4 2 4 0 3 2 7 3 7 0 1 4 1 7 2 0 2 4 0 3 0 1 4 7 2 1 0 1 4 1 0 2 0 1 7 4 7 0 7 4 1 3 1 7 2 0 1 7 2 1 3 1 4 2 0 4 1 2 1 0 2 1 4 2 7 2 1 2 0 2 1 4 2 0 4 2 7 2 3 7 0 2 0 3 0 4 0 2 7 0 2 1 0 2 3 1 0 2 0 1 0 2 3 4 0 2 1 0 2 0 4 0 7 3 2 1 2 7 3 2 3 1 2 3 2 7 1 0 2 0 4 0 3 2 3 4 7 3 7 0 3 2 0 4 3 0 1 7 4 7 3 4 7 4 2 4 7 3 2 7 3 7 4 7 3 2 7 1 3 0 2 7 3 0 3 2 4 7 4 1 3 0 3 4 2 4 0 2 1 4 0 1 4 1 2 7 0 2 7 3 2 3 0 2 4 2 7 4 0 4 2 3 7 4 7 3 0 7 1 0 4 1 7 2 4 2 3 1 3 0 2 4 2 3 2 1 0 2 0 3 4 0 2 0 1 2 3 7 1 4 2 4 0 2 1 0 2 3 0 1 0 2 1 0 7 0 3 1 0 2 0 3 1 7 2 7 1 4 0 4 7 2 0 2 1 0 2 4 0 4 7 3 7 4 7 2 4 2 0 3 0 4 3 0 1 0 2 3 0 7 0 1 2 1 4 7 4 2 4 1 0 7 1 0 1 4 0 1 0 2 1 4 3 0 1 0 2 0 1 0 4 0 2 1 0 1 7 1 0 1 4 2 1 0 1 4 0 7 4 2 1 0 2 0 4 0 3 0 4 1 0 7 4 7 3 7 1 4 3 0 2 4 3 4 0 3 0 1 4 1 3 0 2 0 1 0 2 0 4 2 1 0 2 7 3 1 0 3 2 4 7 4 1 0 2 4 0 3 4 2 0 4 2 7 2 1 7 4 7 2 7 3 1 0 3 0 2 4 0 4 3 7 1 4 1 7 0 1 3 1 0 1 2 0 4 2 0 3 0 7 3 2 7 0 2 0 3 0 7 3 2 1 3 4 2 7 4 3 7 4 0 7 1 7 4 3 7 4 7 2 7 1 0 3 0 4 1 7 2 1 7 1 0 1 2 3 1 0 2 0 1 0 7 1 2 4 3 7 1 7 2 1 2 4 0 3 0 2 7 4 1 2 0 1 0 7 0 2 3 0 1 0 2 1 2 3 2 4 3 1 2 3 1 0 2 0 1 0 2 3 7 4 7 3 0 2 0 7 0 1 2 0 7 1 3

Alphabet {0, 1, 2, 3, 4, 7}

size 6 · diameter 7 · record length 575 · 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

575 (was 287) — David Renshaw, 2026-08-19
287 (first) — David Renshaw, 2026-08-18

Comments

David Renshaw · 2026-08-19 14:29 UTC

Found by randomized depth-first search over {0,1,2,3,4,7}, rejecting each appended symbol whenever it closed an additive square. Four searches were run in parallel, combining forward/reversed prefixes of the previous 287-letter witness with fresh starts. This word came from fresh seed 85103 after 2,798,551,273 search nodes. It was independently checked with a separate prefix-sum verifier before submission.

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