Length 416 over {0, 1, 2, 5, 6}

Word of length 416 over {0, 1, 2, 5, 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).

2 5 1 2 1 0 1 6 1 5 6 2 1 6 0 5 0 1 6 0 2 6 5 1 6 5 6 0 5 2 5 6 2 1 6 0 6 1 2 1 0 2 0 6 5 2 6 0 1 0 6 0 5 6 5 2 1 2 0 1 0 5 6 1 2 1 0 2 1 5 1 2 0 1 0 5 0 6 5 2 0 1 2 0 2 6 0 1 0 5 6 2 1 5 6 5 1 5 6 2 0 1 5 0 1 2 0 1 0 5 0 1 0 6 5 2 5 6 5 0 1 2 1 5 1 6 5 6 2 5 6 0 6 2 0 1 6 5 6 1 6 2 6 1 6 0 6 5 6 2 6 5 6 1 5 6 5 0 5 6 2 1 2 6 0 2 0 5 6 5 0 5 6 1 5 6 2 6 5 0 5 6 1 5 0 2 1 2 0 2 1 6 5 0 1 6 2 6 5 6 2 1 2 6 5 6 2 0 1 0 6 1 0 5 6 0 1 0 2 0 1 0 6 1 2 6 0 6 5 0 1 6 1 5 6 1 2 1 0 2 1 2 5 1 0 1 2 0 1 0 5 0 1 0 2 1 0 6 1 6 2 1 2 0 1 5 1 0 1 2 0 5 1 2 6 1 5 1 0 5 1 6 2 6 5 6 2 1 2 6 2 5 1 0 1 2 1 0 6 2 6 5 0 5 6 1 2 1 6 5 6 2 6 5 0 6 5 6 1 6 2 6 1 6 5 6 1 2 0 6 0 2 0 5 6 1 2 6 5 2 5 0 2 5 1 0 2 1 0 1 5 6 5 2 1 0 1 5 0 1 0 2 0 1 0 6 0 1 2 6 5 0 1 0 2 1 2 6 2 5 6 5 1 2 6 1 6 5 0 1 5 0 2 0 1 0 5 0 1 6 5 6 2 5 6 0 1 0 5 0 2 6 0 2 0 1

Alphabet {0, 1, 2, 5, 6}

size 5 · diameter 6 · record length 416 · 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

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

Comments

David Renshaw · 2026-08-19 15:40 UTC

Found by randomized depth-first search over {0,1,2,5,6}, rejecting an appended symbol whenever it closed an additive square. Four branches ran in parallel: two fresh starts and two branches from rank-mapped prefixes of nearby five-letter records. This 416-letter word came from fresh seed 89103 with a 30-billion-node search cap.

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