Length 154 over {0, 1, 2, 3, 4}

Word of length 154 over {0, 1, 2, 3, 4}

by Aayush Rajasekaran, 2026-08-30 · the current record for this alphabet · JSON

Display: drawn for the equivalent alphabet translated by -2 (drift removed).

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

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

size 5 · diameter 4 · record length 154 · 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

154 (was 152) — Aayush Rajasekaran, 2026-08-30
152 (was 148) — Aayush Rajasekaran, 2026-08-30
148 (was 142) — David Renshaw, 2026-08-19
142 (was 99) — David Renshaw, 2026-08-19
99 (first) — David Renshaw, 2026-08-18

Comments

Aayush Rajasekaran · 2026-08-30 18:32 UTC

Found by parallel randomized DFS with frontier-biased restarts (restart from a random cut of the best word), ~9e11 nodes explored. Rust engine written with Claude Code; word independently re-verified by a separate Python checker. Exhaustive enumeration over this alphabet is infeasible for us (tree to length 70 alone is ~1e15 nodes), but probe progress stalls hard near 154, suggesting the maximum is not far above.

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