Additive Squares

Word of length 2240 over {0, 1, 4, 9, 18}

by Aayush Rajasekaran, 2026-08-26 · the current record for this alphabet · JSON

Display: drawn for the equivalent alphabet translated by -6 (drift removed); downsampled ×2.

0 18 9 1 4 1 9 18 1 18 0 1 18 9 18 1 18 9 4 0 4 9 18 1 9 18 9 0 4 0 1 0 9 4 9 1 4 18 0 9 4 0 1 0 4 18 4 1 4 9 0 4 1 0 1 9 1 0 1 4 1 0 18 4 1 18 4 9 4 18 4 0 9 1 4 18 0 9 4 18 0 4 0 9 4 1 0 18 1 4 1 18 0 18 4 1 9 0 18 1 9 1 4 1 0 4 18 1 4 1 0 4 9 4 1 9 18 9 4 18 9 18 0 18 1 0 9 18 9 0 9 4 18 4 9 0 1 9 1 4 9 1 9 18 1 18 4 1 4 9 18 1 9 1 4 9 4 0 18 0 4 9 4 1 0 4 9 4 18 9 4 1 9 0 1 9 1 4 1 9 1 18 1 9 1 4 0 18 4 0 9 18 0 4 18 1 9 18 1 4 0 4 1 18 1 0 1 4 9 0 4 18 9 1 0 9 4 18 4 0 18 0 9 18 0 18 4 18 0 1 18 4 9 4 0 1 9 1 0 18 1 9 1 4 9 1 18 0 18 4 18 0 9 18 0 1 9 4 9 0 18 9 18 4 9 18 1 18 4 9 0 9 1 9 18 9 0 9 18 9 4 9 0 4 0 18 4 1 0 18 0 1 0 9 4 18 1 4 9 0 9 4 18 9 4 9 0 9 4 18 1 0 4 0 18 0 1 0 9 1 18 1 9 1 18 4 18 9 4 18 1 9 4 9 18 9 0 4 1 9 18 0 9 0 4 0 9 18 0 1 0 18 4 18 1 0 1 4 1 0 18 9 1 0 9 4 9 0 1 0 9 0 1 4 18 9 1 18 9 18 0 18 4 1 9 4 1 4 0 18 0 1 18 9 18 4 0 9 4 18 4 9 0 1 0 18 0 1 4 0 18 1 0 18 9 18 4 0 9 4 1 4 9 18 0 1 0 9 0 1 4 1 0 9 1 9 4 18 9 18 1 9 1 0 1 9 4 0 1 9 18 4 9 4 0 18 0 9 0 4 1 0 1 18 1 0 1 9 0 4 9 0 1 9 0 9 18 0 18 4 1 0 4 18 0 9 4 18 9 18 1 0 4 18 9 0 4 0 9 1 18 1 0 1 4 0 4 9 0 1 0 18 0 1 4 18 0 1 0 9 1 18 1 0 1 4 1 0 18 0 1 4 9 4 18 0 4 0 1 18 9 18 0 9 18 4 0 4 9 4 18 9 1 9 4 18 0 1 9 0 18 1 18 0 18 4 0 18 9 0 4 1 4 9 0 9 18 0 1 0 18 0 9 18 1 18 9 18 1 4 1 0 18 9 4 9 0 9 1 4 1 9 18 1 4 1 9 0 9 1 18 4 18 0 4 0 9 4 9 1 0 18 9 18 1 9 18 0 1 9 4 18 4 0 18 4 1 18 1 0 1 9 18 0 18 1 4 18 0 18 4 18 9 4 1 4 18 1 18 9 18 1 0 9 18 4 9 0 4 0 18 1 0 9 18 1 0 18 1 4 1 18 1 9 4 0 4 1 9 18 9 4 0 1 0 4 0 1 9 4 9 1 9 0 4 18 4 0 1 18 0 9 18 9 1 9 0 18 0 4 9 4 1 9 1 0 1 4 0 9 0 4 0 1 4 0 18 4 18 9 0 4 1 18 0 1 4 0 1 0 9 1 0 18 1 18 4 9 1 0 4 0 9 18 4 18 0 4 1 9 18 0 1 4 0 1 18 1 4 1 18 9 4 18 9 0 1 18 0 18 4 1 4 18 9 18 0 18 9 4 9 18 9 0 18 0 4 9 0 1 9 1 18 9 4 9 1 4 0 1 0 18 9 1 18 9 4 18 1 18 4 18 1 0 18 9 0 18 0 1 18 9 18 4 18 9 18 0 4 18 4 9 1 9 18 9 4 18 1 4 1 0 18 4 9 4 18 4 0 18 9 1 0 9 18 4 18 9 18 1 4 18 9 4 18 4 0 9 18 9 1 9 18 9 4 18 9 18 0 18 1 18 9 18 0 18 9 4 18 4 0 18 1 9 0 4 18 9 18 0 1 18 1 4 0 1 0 18 0 4 0 18 0 1 18 4 0 4 18 9 4 1 18 9 1 9 0 18 9 1 4 9 0 9 18 4 18 9 1 0 4 9 0 18 4 0 9 4 0 1 0 9 18 1 4 0 1 9 4 1 0 4 0 9 4 1 18 0 1 18 9 18 1 0 1 9 4 1 4 18 4 0 18 9 18 1 18 0 18 4 9 4 1 0 1 9 1 18 0 1 4 18 1 0 1 9 1 18 9 18 0 4 18 4 1 9 18 1 0 18 1 4 18 9 18 4 18 1 4 18 9 18 0 9 4 9 1 4 1 0 1 9 4 0 18 1 18 0 4 18 1 9 1 4 1 18 4 18 9 1 9 18 0 18 9 18 4 18 0 9 0 18 4 0 18 1 9 4 1 18 1 9 4 0 4 9 18 0 4 1 18 1 0 9 0 1 0 9 18 9 0 1 9 18 4 0 1 0 4 0 1 18 9 4 0 1 0 18 0 4 0 1 4 18 9 4 1 0 4 1 18 0 18 9 18 1 18 0 1 18 1 9 1 0 9 1 4 1 18 1 0 1 4 9 0 4 9 4 18 0 4 18 4 1 4 0 1 18 1 4 18 9 18 4 1 4 9 18 9 0 18 4 1 4 0 4 18 4 9 0 18 1 9 18 4 0 18 9 4 18 0 4 1 0 1 18 1 4 1 0 1 9 1 18 1 9 0 4 0 1 0 4 9 1 9 4 9 18 9 0 9 1 0 1 4 0 4 9 0 9 1 9 18 4 9 18 1 9 18 4 9 1 4 0 18 0 4 0 1 4 0 4 9 1 18 9 0 1 0 4 0 1 0 9 18 0 4 9 18 9 1 4 1 0 1 18 9 4 1 18 1 0 18 4 1 4 9 4 1 4 0 1 4 9 0 18 9 0 1 0 4 9 18 0 18 9 18 0 1 18 1 4 0 4 18 1 18 0 1 18 4 1 18 9 18 0 18 9 18 4 1 18 4 18 9 4 9 1 18 4 1 9 0 9 18 9 1 4 9 4 0 9 0 1 9 1 4 0 9 18 0 1 0 9 0 4 9 1 9 4 9 0 18 1 18 9 18 4 1 18 1 0 1 18 1 4 9 18 9 4 0 4 9 4 0 1 9 4 0 18 1 18 9 18 1 0 9 0 1 0 4 0 1 0 18 0 4 1 0 4 9 4 18 0 9 0 4 0 18 0 1 18 9 18 4 0 18 0 1 4 0 4 9 1 4 18 4 0 4 9 4 1 4 0 1 18 1 4 0 4 1 9 1 0 4 1 0 9 0 4 0 18 0 9 0 4 0 1 0 9 0 1 18 1 4 9 18 1 9 1 0 18 1 9 0 4 9 4 1 9 4 0 9 1 0 9 0 4 1 18 9 0 1 9 18 1 18 0 18 9 0 9 1 18 0 9 4 18 9 18 1 4 0 1 0 9 4 9 1 4 1 18 4 0 18 9 18 0 18 1 18 0 4 9 4 18 4 0 18 4 18 1 4 0 4 1 9 18 9 1 0 1 18 0 4 0 1 4 1 18 4 1 0 1 4 9 0 4 0 1 0 4 18 0 4 1 0 1 9 0 4 1 9 0 9 4 9 18 1 18 0 18 9 0 1 0 4 18 4 1 9 0 1 4 9 4 0 4 9 4 18 4 0 1 4 1 18 9 4 9 18 0 18 9 18 0 4 1 4 0 18 0 4 0 1 0 9 0 4 0 1 18 1 0 1 9 18 0 9 0 4 1 9 0 9 4 9 18 9 0 9 1 4 1 9 0 1 4 0 4 18 0 4 9 4 0 4 1 9 1 0 4 1 4 18 4 0 4 1 4 18 9 1 0 4 9 0 4 0 1 9 18 1 0 1 9 1 4 9 18 9 0 18 9 1 0 4 1 0 1 18 1 0 4 0 1 0 9 0 4 1 0 1 18 1 4 9 4 18 4 9 1 9 0 9 1 18 9 1 0 4 0 9 0 1 4 9 4 0 18 1 9 18 0 4 0 1 4 9 4 1 4 0 1 9 1 0 1 4 18 0 9 1 0 1 4 1 0 1 18 4 1 0 18 9 0 4 9 1 0 4 1 0 1 9 0 4 18 0 1 0 9 0 18 1 18 4 0 1 0 4 9 0 4 1 4 0 18 0 1 4 0 9 1 0 4 1 4 9 1 0 4 1 18 1 4 1 9 0 4 0 9 18 0 18 1 9 18 9 4 9 0 9 1 4 1 9 1 4 0 4 9 18 9 4 0 4 1 0 9 1 4 18 9 18 4 0 4 9 18 1 4 1 18 1 4 0 1 18 1 0 1 9 0 4 1 18 0 18 4 9 4 1 18 0 1 0 4 9 1 0 1 4 0 1 18 4 9 0 18 0 4 1 0 4 0 9 0 1 18 1 0 4 1 0 9 0 4 9 18 0 1 0 9 4 1 9 1 0 9 1 4 18 4 9 18 9 1 4 18 4 0 4 9 0 4 1 4 0 9 18 9 1 18 0 18 4 9 18 0 18 1 0 9 4 9 1 18 1 4 9 0 18 0 9 0 18 4 9 0 1 0 9 18 1 9 1 4 18 0 1 9 1 18 4 1 4 0 1 0 9 1 9 4 9 1 0 18 0 4 0 9 0 4 1 0 1 9 1 0 1 18 0 1 0 9 4 18 4 9 0 9 1 4 18 4 0 1 4 1 18 1 9 18 4 0 4 9 18 9 1 4 18 0 4 0 1 0 4 18 4 1 4 0 4 1 9 1 0 18 9 0 1 0 4 0 18 1 4 0 1 9 1 0 1 4 1 18 0 4 1 4 0 4 9 4 0 1 0 18 9 0 1 4 18 1 18 0 9 0 4 9 0 1 0 18 1 4 1 18 1 0 1 9 1 0 1 4 0 4 9 1 18 1 0 4 0 1 9 0 4 0 18 4 0 4 9 1 4 1 0 1 18 4 0 1 0 9 0 1

← previous record (1966)

Alphabet {0, 1, 4, 9, 18}

size 5 · diameter 18 · record length 2240 · JSON

open No exhaustive search has settled this alphabet; the record is a lower bound on the (possibly infinite) maximum.

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Record history

• 2240 (was 1966) — Aayush Rajasekaran, 2026-08-26
• 1966 (was 1506) — Aayush Rajasekaran, 2026-08-20
• 1506 (first) — David Renshaw, 2026-08-18

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