Additive Squares

Word of length 1562 over {0, 1, 3, 7, 15}

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.

3 7 1 3 15 3 0 15 7 3 1 3 7 3 15 3 7 1 0 1 7 15 0 7 15 7 1 15 0 15 3 15 1 15 3 7 3 1 15 0 15 3 7 0 7 3 1 15 7 15 0 7 3 15 0 1 0 3 0 1 7 1 15 7 15 3 0 3 15 1 0 15 1 7 3 15 0 3 1 3 15 7 3 7 0 15 7 3 15 3 0 1 7 3 1 7 15 7 0 7 3 0 7 1 7 3 1 15 7 3 1 0 15 0 3 0 1 0 7 3 1 3 0 1 0 7 3 0 7 15 3 7 3 1 0 3 1 3 7 3 15 0 15 1 15 7 1 0 1 15 3 15 7 3 15 1 15 3 7 0 15 3 7 15 7 1 3 1 15 1 3 7 0 15 3 1 3 7 15 1 3 7 0 7 15 3 7 0 3 7 3 1 0 7 3 0 15 0 7 3 1 0 7 15 7 1 7 3 15 7 1 15 7 0 7 15 1 15 3 1 3 0 3 1 15 7 1 7 0 15 1 3 15 7 3 7 1 3 15 7 15 0 15 3 7 3 15 3 1 15 7 3 1 0 1 3 15 7 1 15 0 15 7 15 1 7 1 3 1 15 1 0 15 7 0 7 1 7 3 0 7 1 3 1 7 1 3 15 7 3 1 3 15 7 15 1 0 3 15 0 15 7 3 7 15 7 3 0 3 1 7 15 7 3 0 15 7 0 15 1 15 3 15 7 15 3 1 15 3 15 7 15 0 1 15 0 15 7 15 0 1 3 0 7 15 3 15 7 1 15 1 0 1 7 1 3 0 1 3 15 0 7 3 15 3 1 0 7 15 7 3 1 7 15 0 1 7 1 15 3 15 0 15 7 15 1 15 0 15 7 15 0 15 3 15 1 15 7 3 0 1 15 3 1 15 1 0 1 15 1 7 0 7 15 7 3 15 3 1 15 7 1 0 7 15 3 15 0 15 3 7 0 7 15 1 15 7 15 3 15 7 15 1 15 0 15 7 15 0 15 3 15 7 0 15 0 1 7 1 3 15 1 15 7 15 3 0 7 3 1 3 15 0 15 7 15 0 15 1 15 0 3 0 7 1 7 15 0 15 1 7 15 0 7 0 1 7 0 7 3 1 0 3 7 3 15 3 7 0 1 7 1 3 7 0 1 0 7 0 3 0 7 1 15 3 15 1 15 3 0 15 3 1 15 3 7 3 1 0 1 7 1 3 7 15 3 7 3 0 15 7 1 7 15 3 7 15 0 15 1 3 15 1 7 3 0 1 0 3 15 0 15 7 0 7 3 0 1 7 1 3 7 3 15 0 15 1 15 7 3 15 7 15 1 7 1 3 0 1 7 3 15 7 15 1 15 0 15 1 15 7 15 3 15 1 3 0 1 3 1 7 3 1 3 0 3 15 0 7 3 7 15 1 0 7 15 1 7 1 0 3 15 0 3 7 15 7 1 0 7 3 0 1 15 0 1 0 3 0 1 7 3 0 1 15 7 0 15 3 15 1 15 0 15 1 15 3 1 15 1 7 3 0 1 3 15 0 15 7 15 0 3 0 7 1 0 15 3 0 3 7 3 1 3 0 7 1 0 7 15 7 0 3 0 1 3 1 7 0 7 3 1 3 15 3 1 7 15 1 15 0 15 3 0 7 1 3 1 0 3 0 15 1 15 3 0 7 1 15 0 7 0 1 3 1 7 15 1 0 7 1 3 0 3 15 7 0 1 0 3 7 0 1 3 1 0 1 7 1 15 1 0 3 0 1 7 0 3 7 0 15 0 7 3 7 15 1 15 3 1 3 0 15 7 1 7 3 1 0 1 3 1 7 3 1 15 1 7 0 1 15 1 3 1 0 7 3 1 0 1 3 1 15 0 3 0 1 0 7 3 1 7 0 7 1 3 1 15 7 0 1 7 0 3 1 0 1 7 1 0 1 15 3 0 1 3 1 7 3 15 1 0 15 0 3 15 7 3 7 0 3 1 15 0 1 0 7 0 1 0 3 0 15 7 0 3 1 0 1 7 0 1 15 0 15 7 15 0 15 3 0 7 15 0 1 3 15 1 0 7 15 3 0 1 0 3 0 7 3 1 3 7 15 1 7 3 7 1 0 3 0 1 0 7 1 7 3 7 15 0 1 0 7 1 3 1 15 1 3 0 15 1 0 15 7 15 1 7 3 0 15 3 1 15 3 15 0 15 7 15 1 0 3 1 0 15 0 7 15 1 15 0 7 15 7 3 1 3 0 7 15 1 15 3 7 15 7 1 7 0 15 1 15 0 15 7 1 7 3 0 1 7 15 3 15 1 15 3 0 1 0 7 1 0 3 0 1 15 1 3 15 7 3 1 3 0 1 3 1 7 0 7 1 7 3 15 3 1 15 0 15 7 0 1 7 3 7 15 3 0 15 1 3 0 1 3 7 0 15 1 3 1 7 15 3 15 0 15 1 3 15 7 15 0 1 7 15 1 15 3 1 7 3 1 3 0 1 3 15 0 7 1 15 3 15 1 7 0 7 3 0 7 0 1 3 1 7 3 7 0 7 3 1 3 7 3 1 15 0 7 3 1 7 0 3 0 1 0 7 0 1 15 1 3 1 0 7 1 7 3 1 3 0 3 1 7 0 7 15 1 3 1 0 15 7 15 1 15 3 7 3 1 0 15 0 3 0 15 1 7 15 3 1 15 3 15 0 15 7 3 15 1 3 15 3 7 0 7 1 3 1 7 0 1 0 3 0 1 7 15 0 1 7 0 7 3 0 15 0 7 0 15 0 1 15 0 7 15 1 7 3 1 15 7 15 3 7 15 7 1 3 1 0 15 0 7 3 1 7 3 0 15 3 1 15 3 7 15 3 15 0 7 15 7 1 15 0 15 7 0 15 3 1 15 0 1 15 7 15 1 3 7 3 0 1 0 7 3 7 1 3 15 3 7 0 1 0 15 1 0 7 0 1 0 3 0 15 3 1 7 15 3 15 0 7 15 7 1 3 1 15 3 15 7 15 3 15 1 15 0 15 3 7 15 1 15 3 1 0 1 15 0 15 7 15 3 15 1 7 15 1 3 1 7 15 0 15 3 7 3 15 1 3 7 15 0 1 3 1 15 1 0 1 15 7 0 1 15 0 15 7 0 3 0 15 1 15 7 15 1 15 3 1 3 7 1 7 15 0 7 15 1 3 7 15 0 7 3 7 15 3 15 1 15 7 15 1 15 0 15 7 3 15 7 0 15 0 1 15 0 3 15 0 7 15 7 3 15 7 15 0 3 15 1 0 3 1 0 1 15 7 15 3 0 15 3 15 1 0 1 15 7 3 15 1 15 0 15 1 15 7 15 0 7 0 3 15 3 0 1 0 15 0 1 3 1 0 15 1 0 7 15 0 3 7 15 7 1 3 1 15 0 15 3 0 15 7 3 1 3 7 15 3 15 0 15 3 7 1 15 3 15 7 15 0 7 3 7 0 1 3 7 3 0 3 15 0 15 7 15 3 15 7 15 1 15 3 15 0 15 3 7

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Alphabet {0, 1, 3, 7, 15}

size 5 · diameter 15 · record length 1562 · 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

• 1562 (was 1411) — Aayush Rajasekaran, 2026-08-26
• 1411 (was 896) — David Renshaw, 2026-08-20
• 896 (first) — David Renshaw, 2026-08-18

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