Additive Squares

Word of length 62 over {0, 1, 2, 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).

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

Alphabet {0, 1, 2, 4}

size 4 · diameter 4 · record length 62 · JSON

closed The exact maximum additive-square-free word length over this alphabet is 62. exhaustive search (search.c), 19,097,777 nodes

Closure claims

• accepted max 62 claimed by unknown, 2026-08-18 — exhaustive search (search.c), 19,097,777 nodes

Record history

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

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