Additive Squares

Word of length 50 over {0, 1, 2, 3}

by David Renshaw, 2026-08-18 · the current record for this alphabet · JSON

Display: drawn for the equivalent alphabet translated by -1 (drift removed).

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

Alphabet {0, 1, 2, 3}

size 4 · diameter 3 · record length 50 · JSON

closed The exact maximum additive-square-free word length over this alphabet is 50. exhaustive search (search.c), 187,788 nodes

Closure claims

• accepted max 50 claimed by unknown, 2026-08-18 — exhaustive search (search.c), 187,788 nodes

Record history

• 50 (first) — David Renshaw, 2026-08-18

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