Length 409 over {0, 1, 2, 3, 6}

Word of length 409 over {0, 1, 2, 3, 6}

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

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

1 3 6 3 2 3 1 3 6 1 3 0 6 3 1 6 3 6 2 3 0 6 1 2 0 1 6 1 0 2 0 3 2 0 6 0 3 0 6 1 0 6 0 3 6 0 2 6 0 3 1 6 3 0 6 3 6 1 6 3 6 0 3 2 6 2 0 2 1 2 6 3 2 0 2 3 1 2 0 2 3 0 6 2 6 3 6 2 1 2 0 6 0 3 6 3 2 1 0 1 3 0 1 6 0 2 0 1 3 0 1 0 2 0 1 3 2 6 3 2 0 1 0 3 2 0 3 0 6 1 6 0 3 2 0 3 6 3 1 6 0 6 3 6 2 6 3 6 1 0 2 0 3 6 2 0 6 2 6 1 2 0 2 3 2 1 0 2 0 3 2 6 3 2 0 3 1 0 2 6 0 3 6 3 1 3 6 0 6 2 6 0 6 1 3 0 3 2 6 1 2 6 3 6 1 6 3 6 0 6 2 6 3 6 0 1 0 2 0 1 0 3 6 0 6 2 6 3 6 1 2 3 1 6 0 6 3 6 2 6 3 6 0 6 3 6 1 6 3 6 0 6 3 6 2 6 3 6 0 3 1 6 0 2 6 3 6 1 6 2 3 6 3 0 1 0 2 6 3 6 2 1 6 0 1 0 2 1 2 6 1 3 2 1 0 2 0 3 6 1 6 3 6 0 6 3 6 2 3 6 3 1 3 6 3 0 2 6 3 0 3 6 3 0 1 0 2 1 0 6 3 6 2 3 0 2 0 1 0 3 6 1 0 2 0 1 0 2 3 0 2 0 1 0 2 6 3 2 0 6 2 3 1 6 2 3 0 2 6 0 6 1 6 3 6 1 6 2 6 0 1 0 2 1 0 6 1 0 1 3 2 6 3 1 3 0 1 0 2 1 0 6 1 0 3 0 2 0 6

Alphabet {0, 1, 2, 3, 6}

size 5 · diameter 6 · record length 409 · 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

409 (first) — David Renshaw, 2026-08-19

Comments

David Renshaw · 2026-08-19 14:49 UTC

Found by randomized depth-first search over {0,1,2,3,6}, rejecting an appended symbol whenever it closed an additive square. Four branches ran in parallel for about ten minutes: two fresh starts and two branches based on a 42-letter rank-mapped, reversed prefix of the {0,1,2,3,4} record. This 409-letter word came from fresh seed 86104 with a 30-billion-node search cap.

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