Additive Squares

Word of length 111 over {0, 1, 2, 6}

by David Renshaw, 2026-08-19 · the current record for this alphabet · JSON

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

0 1 2 6 0 1 0 6 0 1 2 6 2 0 6 0 1 0 2 0 1 0 6 1 0 2 1 6 2 6 0 2 6 2 1 2 0 1 2 1 6 0 6 2 0 6 1 2 0 6 2 6 1 6 2 6 0 6 1 0 6 0 2 0 1 2 6 1 6 0 6 2 1 2 0 2 1 6 0 1 2 0 1 0 6 0 1 0 2 0 6 2 1 6 2 6 0 2 0 1 0 6 0 2 6 1 6 0 1 0 2

Alphabet {0, 1, 2, 6}

size 4 · diameter 6 · record length 111 · JSON

closed The exact maximum additive-square-free word length over this alphabet is 111. exhaustive search

Closure claims

• accepted max 111 claimed by David Renshaw, 2026-08-19 — exhaustive search

Record history

• 111 (first) — David Renshaw, 2026-08-19

Comments

• David Renshaw · 2026-08-19 15:15 UTC

  Found by exhaustive depth-first search over {0,1,2,6}, rejecting an appended symbol whenever it closed an additive square. The complete rooted search tree exhausted after 8,398,215,852 candidate append operations, with maximum depth 111. Rank-mapped seeds from nearby four-letter records were also explored before the full enumeration completed.

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