Additive Squares

Word of length 55 over {0, 1, 3, 4}

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

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

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

Alphabet {0, 1, 3, 4}

size 4 · diameter 4 · record length 55 · JSON

closed The exact maximum additive-square-free word length over this alphabet is 55. exhaustive search (search.c), 659,726 nodes

Closure claims

• accepted max 55 claimed by unknown, 2026-08-18 — exhaustive search (search.c), 659,726 nodes

Record history

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

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