Additive Squares

Word of length 86 over {0, 1, 2, 5}

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

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

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

Alphabet {0, 1, 2, 5}

size 4 · diameter 5 · record length 86 · JSON

closed The exact maximum additive-square-free word length over this alphabet is 86. exhaustive search (search.c), 299,596,818 nodes

Closure claims

• accepted max 86 claimed by unknown, 2026-08-18 — exhaustive search (search.c), 299,596,818 nodes

Record history

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

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