Additive Squares

Word of length 1495 over {0, 1, 3, 7, 12}

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

05001000-300-200-1000 position in word → partial sum

Display: drawn for the equivalent alphabet translated by -5 (drift removed); downsampled ×2.

0 1 0 7 3 1 7 0 7 1 3 12 7 0 7 12 7 1 12 7 3 7 1 3 0 3 1 3 12 0 3 0 1 3 0 7 0 12 1 7 0 1 7 1 12 0 3 12 1 0 7 12 3 7 12 1 12 7 0 12 3 1 0 1 7 1 12 7 1 7 3 1 0 1 3 7 12 7 0 7 12 3 0 12 3 1 12 7 0 12 7 12 1 7 12 3 12 1 0 12 1 3 7 0 7 1 12 7 3 12 7 12 1 0 12 0 7 0 12 3 0 1 0 12 0 3 12 1 3 7 12 7 0 1 7 3 0 1 0 7 12 0 12 3 0 7 3 12 3 0 3 1 3 7 1 3 1 0 3 12 1 7 1 0 7 1 3 0 1 0 7 12 1 0 1 3 0 1 0 7 0 1 0 3 0 7 3 1 12 3 0 1 0 7 3 1 0 1 7 12 7 0 12 3 0 1 0 7 0 3 0 1 3 7 3 0 1 3 12 1 3 1 0 7 0 1 3 12 0 12 1 0 12 7 12 1 0 12 0 3 1 7 1 3 1 0 3 0 7 12 0 7 1 12 7 3 12 7 12 0 7 0 3 7 3 12 7 0 7 12 7 1 12 7 0 1 0 7 3 1 3 7 12 7 3 0 12 0 7 0 1 0 12 3 0 3 1 3 7 1 3 12 3 7 1 3 0 12 7 12 0 12 3 0 1 3 0 7 3 1 3 0 12 1 12 7 3 12 1 3 12 3 7 3 12 3 1 0 7 12 1 12 7 3 7 12 0 7 12 1 12 3 7 3 0 7 3 1 7 3 0 12 1 7 12 3 1 12 1 0 3 1 0 1 7 12 3 7 12 7 0 7 1 0 7 3 7 0 7 12 3 12 1 3 0 3 12 7 12 3 12 1 7 12 0 12 7 12 3 12 0 7 12 7 3 7 12 1 7 12 7 0 7 12 3 0 1 7 1 0 12 1 7 0 3 12 0 7 0 12 3 12 7 12 0 12 7 1 12 7 0 12 7 3 0 12 1 7 1 12 3 1 0 1 12 7 0 12 3 0 3 1 12 1 3 0 1 3 1 7 3 12 7 0 12 7 3 12 7 12 1 3 1 12 7 0 12 0 1 0 7 1 3 0 12 7 0 1 12 1 3 12 7 0 7 1 7 0 12 1 0 1 3 1 7 0 12 7 0 1 0 7 0 12 3 1 0 3 7 0 7 12 1 7 0 12 7 12 1 12 3 0 12 0 7 3 7 1 7 0 12 1 0 3 12 7 0 7 12 1 0 1 3 0 3 12 1 3 0 3 1 3 7 0 3 0 12 0 7 1 0 1 3 1 0 7 0 1 0 3 1 0 12 0 7 0 12 0 3 0 1 0 3 0 7 0 12 3 1 3 7 12 3 12 1 0 3 7 1 0 1 7 12 1 7 3 7 1 7 12 7 1 3 12 3 1 3 7 12 7 0 12 0 3 7 0 3 1 7 0 12 1 12 3 7 3 1 12 3 1 0 3 0 7 0 3 0 12 0 1 3 1 0 1 7 3 0 3 1 12 7 0 1 7 1 12 3 0 12 1 3 1 12 7 3 7 12 7 1 0 12 7 1 7 3 12 3 0 12 1 3 7 12 3 0 1 3 1 7 1 0 7 0 12 3 1 7 3 12 0 12 7 12 3 0 7 3 12 1 0 1 12 1 7 12 3 0 3 12 1 12 7 12 1 12 3 0 1 7 12 3 1 7 3 0 1 7 12 3 0 1 7 0 12 1 7 1 0 3 12 0 3 0 7 0 3 0 12 0 1 12 0 12 3 1 3 0 12 7 12 0 1 3 12 1 3 7 12 1 12 3 0 3 12 3 1 12 3 7 12 7 0 3 1 12 7 12 3 7 12 7 0 7 12 7 3 1 0 3 0 12 1 3 12 3 7 12 1 12 7 12 1 0 7 12 3 7 12 7 0 7 12 3 7 3 1 12 7 3 1 0 1 3 12 1 3 0 1 7 0 3 12 7 3 0 3 1 0 3 12 3 7 12 7 0 3 12 0 12 7 12 1 3 7 0 12 3 12 7 12 3 1 12 1 0 12 7 12 3 7 0 3 12 3 7 1 0 3 12 7 3 12 3 0 7 0 12 3 12 0 12 1 12 7 12 3 12 7 12 0 7 12 7 3 7 12 1 12 3 12 0 7 3 0 1 0 12 0 3 12 0 7 0 12 3 12 7 1 12 3 7 3 1 7 0 12 3 1 7 3 7 12 3 12 0 12 7 12 3 12 1 7 1 0 7 12 3 12 7 0 12 3 7 3 0 1 7 12 7 3 1 12 3 12 7 3 7 1 0 12 0 1 7 0 3 1 12 7 3 0 12 7 0 12 0 1 3 1 0 1 7 1 3 1 12 0 1 0 3 7 12 3 12 1 3 1 0 12 7 12 1 7 12 0 1 0 3 7 3 1 12 7 3 1 0 12 7 12 3 7 1 7 12 1 12 3 12 1 7 3 0 3 12 0 12 7 0 12 1 3 1 12 0 12 7 12 3 12 0 1 12 7 3 7 12 7 1 7 12 0 12 7 1 12 7 12 3 1 12 3 12 0 1 12 7 3 0 12 1 3 1 7 1 12 3 1 0 12 0 1 0 3 1 7 1 12 0 3 1 3 12 7 3 7 0 7 1 12 7 3 7 12 1 12 0 1 3 0 1 7 3 1 12 1 0 12 3 0 3 1 3 0 12 0 1 0 3 0 1 7 1 0 3 12 3 0 1 3 0 12 0 1 0 12 7 3 12 0 12 1 7 12 1 3 0 1 12 0 7 0 12 0 3 12 1 12 3 12 0 12 3 1 7 3 0 3 12 3 1 12 1 7 12 7 0 1 12 7 1 12 3 12 0 12 3 12 7 12 0 7 0 1 0 12 3 1 0 1 12 1 0 1 7 12 3 12 0 12 3 7 3 1 3 0 3 12 0 12 1 0 7 3 0 7 0 1 0 7 3 0 12 0 1 7 12 3 7 12 0 12 7 1 7 0 1 7 12 3 7 1 3 1 12 0 3 1 0 3 0 12 3 7 1 0 1 3 0 1 12 0 1 0 3 1 0 1 7 1 0 1 3 0 3 7 1 12 3 0 1 3 0 3 7 0 7 12 3 1 3 7 1 3 12 0 1 12 1 3 12 7 1 0 1 12 7 3 7 1 12 7 12 0 12 7 1 12 3 7 3 0 7 1 3 12 7 3 1 0 3 1 3 12 7 3 7 0 3 7 3 12 1 12 0 3 0 12 1 0 1 3 0 3 7 0 1 7 3 0 12 7 3 7 0 3 1 7 12 7 3 12 3 1 12 3 7 12 3 0 1 7 3 12 0 12 1

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Alphabet {0, 1, 3, 7, 12}

size 5 · diameter 12 · record length 1495 · JSON

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

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