Length 750 over {0, 1, 2, 3, 4, 5, 7}

Word of length 750 over {0, 1, 2, 3, 4, 5, 7}

by David Renshaw, 2026-08-19 · JSON

This is a historical record from 2026-08-19, superseded on 2026-08-26 by length 1102 — jump to the current record (1559).

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

2 1 5 1 4 7 1 0 5 4 0 4 7 3 1 5 7 3 5 3 0 3 1 5 7 3 5 4 7 1 0 5 4 7 1 5 7 2 7 3 5 2 1 7 4 7 2 4 0 2 1 5 7 3 5 0 2 0 1 4 2 5 0 1 0 7 1 2 0 7 2 7 4 2 5 0 5 2 1 4 3 7 3 4 2 1 4 3 7 2 4 1 2 4 7 2 7 1 7 3 4 5 7 1 7 5 7 1 3 2 4 7 0 5 3 7 5 3 5 4 1 5 3 1 2 3 1 0 2 1 2 3 4 7 5 0 5 3 1 4 5 4 3 2 7 5 7 4 5 7 1 4 5 2 0 1 0 2 0 7 5 7 3 5 2 7 5 7 4 7 0 7 2 1 7 2 4 3 7 5 4 7 5 1 5 7 5 4 7 4 1 4 0 4 2 4 7 3 2 5 4 7 3 7 4 7 2 4 7 3 5 0 5 2 7 3 5 7 3 7 2 7 4 7 3 7 0 5 7 5 3 5 7 4 7 3 7 5 1 7 4 3 0 5 3 1 0 1 2 4 0 1 7 2 7 5 7 1 7 3 7 2 7 0 2 7 5 1 2 0 2 1 2 0 4 0 5 2 1 4 7 0 3 7 5 2 4 5 2 1 2 4 0 3 0 1 0 3 2 4 5 2 1 4 2 0 4 1 2 1 7 2 4 3 1 0 7 4 7 2 7 5 3 4 2 1 3 7 5 4 1 0 2 3 7 3 1 2 1 3 1 2 0 7 1 2 0 1 4 0 1 0 2 0 5 1 3 5 7 4 5 1 0 5 2 0 1 4 0 1 0 2 1 4 2 0 1 2 7 5 3 0 1 0 4 1 0 2 5 2 0 1 0 2 0 3 1 0 2 1 4 0 7 2 0 1 0 4 0 2 1 4 5 7 5 1 0 1 3 0 1 4 2 1 0 4 0 1 0 2 7 1 2 5 1 0 1 3 1 4 7 5 3 5 4 2 1 4 3 7 2 3 7 5 4 5 3 4 3 1 0 1 2 0 7 0 2 0 1 3 7 2 1 4 2 0 2 7 3 7 5 7 4 2 7 3 5 7 4 5 7 3 1 4 1 3 0 5 2 1 3 2 0 7 1 3 7 3 0 7 3 1 5 3 5 7 5 0 7 5 7 4 5 7 5 2 5 3 1 3 7 5 4 3 7 3 1 2 1 0 2 7 4 0 2 7 5 3 5 7 4 3 1 5 7 3 7 2 7 5 7 3 7 5 7 4 7 2 5 7 3 7 5 7 2 1 2 4 7 0 4 0 2 5 7 1 7 4 7 0 7 3 2 5 7 4 0 7 1 4 0 2 1 5 1 2 3 4 3 2 7 5 3 2 7 3 4 1 5 7 5 3 7 5 7 2 7 3 1 5 7 1 4 1 3 7 3 5 4 7 5 7 3 1 2 1 4 2 7 5 2 1 4 0 3 7 1 0 4 0 1 0 2 1 4 3 7 2 3 0 3 4 3 5 4 7 0 7 4 7 2 0 5 7 0 3 0 2 3 7 4 5 1 0 7 1 2 1 0 2 0 3 1 3 7 3 0 1 0 3 0 1 4 2 5 4 7 5 4 0 2 4 1 2 5 1 0 5 2 1 2 3 4 5 4 7 4 0 7 5 4 0 5 2 0 3 5 0 2 7

Alphabet {0, 1, 2, 3, 4, 5, 7}

size 7 · diameter 7 · record length 1559 · 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

1559 (was 1102) — David Renshaw, 2026-09-09
1102 (was 750) — David Renshaw, 2026-08-26
750 (was 625) — David Renshaw, 2026-08-19
625 (first) — David Renshaw, 2026-08-19

Comments

David Renshaw · 2026-08-19 18:14 UTC

Started from the 625-letter record for {0,1,2,3,4,5,7} and used iterated mobility-ordered tail rewriting. Each attempt retained a prefix, regenerated 20 to 350 trailing positions by randomized depth-first search, and kept every equal-length structural alternative or one-position improvement. Seed 93403 reached length 750 after 187 rewrite attempts and 991,375,453 cumulative DFS nodes.

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