Additive Squares

Word of length 2823 over {0, 1, 3, 7, 12, 20}

by Aayush Rajasekaran, 2026-08-20 · the current record for this alphabet · JSON

0500100015002000250005001000 position in word → partial sum

Display: drawn for the equivalent alphabet translated by -6 (drift removed); downsampled ×3.

1 0 3 12 1 3 7 1 20 3 12 20 0 3 7 12 3 20 12 1 20 7 12 20 3 7 0 1 12 0 20 3 12 20 7 3 1 7 0 1 3 20 0 3 7 0 1 3 12 0 1 7 0 3 1 20 12 3 7 12 0 3 20 7 12 20 1 7 20 0 7 3 1 12 0 1 20 0 12 7 20 1 12 20 3 20 12 20 7 0 20 3 20 7 1 12 7 20 3 12 0 7 12 1 3 1 0 12 1 7 0 7 3 20 12 1 20 7 12 20 3 12 0 1 20 3 12 3 0 12 3 7 12 0 1 3 0 7 1 20 0 3 1 12 20 1 3 7 20 1 0 7 3 12 20 1 7 0 20 0 3 1 0 7 0 1 0 3 1 7 3 0 12 1 7 3 7 0 20 12 0 3 1 12 0 20 12 7 20 0 3 7 0 1 3 7 1 20 3 0 20 7 1 12 20 1 0 20 12 3 20 1 0 7 3 1 12 7 1 20 12 20 3 7 20 12 0 20 7 1 20 12 1 3 20 7 12 1 12 3 1 12 20 0 12 3 7 0 1 12 1 0 1 3 0 1 20 0 3 12 0 1 7 12 1 20 12 0 20 1 3 7 0 3 12 0 3 20 1 0 20 12 20 3 1 20 0 20 7 0 1 20 0 3 12 7 20 12 0 7 12 20 7 12 1 20 7 20 0 20 3 7 20 0 12 20 7 20 12 20 1 20 0 12 20 7 12 3 20 0 3 7 20 7 12 3 20 0 12 20 7 12 0 7 3 0 1 3 20 7 12 3 20 1 0 20 12 20 7 12 1 20 3 7 0 20 7 1 20 0 12 1 0 7 3 0 1 12 20 0 20 1 3 20 7 0 20 7 12 1 12 3 0 12 1 7 3 0 3 1 0 3 12 1 0 3 20 0 1 7 3 1 0 12 1 7 20 1 12 3 1 20 0 1 7 20 3 20 12 0 3 1 20 12 1 7 0 3 12 7 12 20 3 1 20 0 7 20 12 20 7 3 20 12 20 7 0 20 12 1 7 3 1 20 7 1 12 7 3 20 12 7 1 12 7 0 1 3 0 7 12 7 0 20 3 12 20 0 20 1 3 7 12 0 20 1 3 20 0 7 1 0 3 1 0 12 7 1 0 3 1 20 12 7 3 20 0 1 7 3 20 12 7 1 0 3 1 7 1 0 3 0 1 0 7 3 1 7 0 7 12 1 3 0 1 12 7 0 7 1 20 3 12 1 7 3 0 1 20 3 12 7 20 12 1 20 7 0 12 1 3 0 3 7 0 12 7 1 12 20 7 20 3 12 20 7 12 0 20 1 20 0 20 3 12 7 3 1 7 20 3 12 7 20 0 12 3 1 0 7 3 1 12 3 0 1 0 7 0 3 1 7 1 20 7 0 20 7 3 0 7 1 12 20 7 0 20 7 3 20 0 20 1 7 0 1 3 0 12 1 3 20 0 7 20 0 1 20 3 12 1 7 20 0 12 20 7 12 3 20 0 20 1 7 20 3 12 20 7 20 12 1 20 0 12 20 1 3 12 0 1 0 7 1 12 3 0 20 1 12 20 7 3 20 0 7 0 12 3 1 7 3 0 7 1 20 12 1 7 3 1 0 12 1 0 20 3 12 20 7 20 0 12 20 1 0 20 3 12 3 0 3 7 0 1 7 3 12 7 20 1 20 3 12 1 20 3 0 3 1 3 7 3 1 0 3 12 7 1 0 3 1 0 1 12 20 0 1 12 3 0 1 7 20 3 0 1 7 12 7 20 0 1 0 20 12 20 1 12 20 3 20 7 0 20 12 20 7 3 20 7 0 1 12 0 20 0 3 0 1 0 7 12 1 20 3 12 1 12 7 0 12 20 12 1 20 7 1 0 12 7 1 20 3 1 7 12 7 3 1 3 0 1 12 7 0 1 0 3 7 3 20 1 7 0 1 3 12 0 3 1 3 20 7 3 12 0 3 20 0 20 1 12 7 0 7 12 7 1 3 12 3 0 1 3 1 7 3 0 12 0 1 3 0 7 1 0 1 3 0 3 7 0 1 3 12 3 0 20 1 3 0 7 12 20 7 0 3 7 1 0 12 1 3 0 1 7 0 3 20 7 12 20 1 20 12 20 0 12 1 20 3 0 1 12 7 1 0 3 20 1 0 12 3 1 12 7 1 20 3 1 0 3 1 7 1 0 3 0 1 12 7 0 1 3 0 7 20 1 3 0 12 1 12 7 1 20 3 12 20 7 0 3 12 0 1 12 20 7 20 12 3 20 0 20 1 3 12 20 3 7 12 3 0 20 12 0 1 3 0 12 7 1 0 3 0 12 0 7 20 0 7 1 3 7 0 12 7 20 12 0 20 1 12 1 0 3 1 12 7 20 1 3 20 12 1 20 0 20 12 20 7 0 20 3 20 0 20 1 3 1 20 12 7 3 20 12 0 3 1 12 0 1 7 12 0 3 1 12 20 1 12 7 0 1 20 7 20 12 20 0 7 1 3 12 7 1 0 7 20 3 1 20 12 0 1 0 3 0 1 7 0 3 1 3 20 1 7 0 3 1 0 12 7 1 3 1 20 3 7 20 0 12 7 3 1 0 12 1 20 0 12 3 20 0 7 20 12 20 7 20 1 20 0 12 1 20 3 0 1 7 3 1 12 0 20 7 0 3 0 1 12 0 3 1 3 7 3 20 1 20 7 20 1 12 7 3 20 1 3 0 1 12 7 12 3 7 1 12 3 1 0 1 3 7 0 12 7 1 3 0 1 20 7 20 12 7 1 12 0 7 3 1 0 3 0 12 1 20 0 1 12 0 3 1 3 7 3 0 7 0 1 0 3 0 1 12 3 12 0 3 12 1 0 1 12 20 7 1 12 0 3 1 0 7 12 0 1 0 12 20 0 12 3 7 12 20 12 0 1 7 1 20 0 3 12 7 0 1 12 20 1 0 7 1 20 0 3 0 1 0 7 1 20 1 12 1 3 1 0 7 3 12 0 1 7 0 1 3 1 0 7 0 3 0 1 0 12 7 3 1 12 1 0 3 1 20 1 0 3 1 0 20 0 3 0 1 0 12 0 3 0 1 0 7 0 12 1 3 20 1 0 20 3 20 12 1 0 7 1 3 12 7 1 12 0 7 3 1 0 7 0 3 12 7 3 1 0 7 3 7 20 1 20 3 20 0 20 1 20 12 1 0 12 1 7 0 3 12 20 0 7 3 0 20 1 0 3 1 12 0 1 7 3 7 0 1 0 3 0 1 7 1 0 3 1 20 0 3 12 0 7 20 0 3 1 0 12 20 3 12 7 3 0 20 1 7 3 0 1 12 0 7 0 3 20 7 20 12 20 0 20 1 20 12 20 7 12 0 20 12 3 20 7 0 12 3 1 7 0 20 12 0 1 0 7 1 3 7 12 0 7 1 20 3 1 12 3 7 1 0 20 3 20 0 20 12 20 3 12 1 20 1 12 1 0 3 1 7 0 12 7 3 12 20 7 0 1 7 3 12 0 3 1 0 7 1 0 12 0 1 3 12 7 3 1 0 1 12 7 1 3 7 0 20 12 20 1 7 12 1 0 3 20 1 0 12 0 1 0 3 1 0 7 1 3 7 12 0 20 12 3 0 7 0 1 0 12 3 0 1 3 7 0 1 0 3 1 12 0 1 20 7 1 3 7 0 3 1 7 12 1 20 3 0 20 12 1 0 7 1 0 3 20 0 12 0 20 1 12 20 3 0 12 20 1 7 3 20 1 0 20 12 20 7 12 20 3 20 0 20 12 0 7 12 20 0 3 1 12 7 0 1 0 3 1 7 3 12 7 0 3 1 7 12 20 1 3 12 0 3 7 0 3 1 0 12 3 0 1 3 1 7 0 12 1 0 20 1 3 7 12 1 7 20 12 7 3 12 20 0 3 7 3 1 7 0 12 3 7 3 1 0 20 1 7 12 3 1 0 3 0 7 0 3 0 1 12 0 1 0 3 1 12 1 3 7 0 3 0 1 3 1 7 0 20 0 12 0 3 7 12 3 20 3 12 1 7 1 0 3 0 12 7 0 1 3 7 1 0 1 12 0 3 20 0 7 0 1 3 0 7 0 12 3 1 0 3 0 7 3 0 1 0 3 0 7 0 12 1 0 1 3 1 7 12 3 0 7 3 0 1 7 12 0 7 1 7 20 3 7 1 12 3 0 7 0 1 7 0 3 1 12 1 7 1 0 7 0 12 1 0 7 3 1 3 20 7 12 20 7 1 20 0 12 1 7 0 1 12 0 3 1 3 20 1 12 20 3 20 7 20 12 7 0 20 3 1 0 3 12 1 0 7 12 1 0 1 3 12 0 1 7 20 12 0 7 0 1 7 12 1 3 7 0 3 1 3 0 12 0 3 0 7 0 20 3 7 0 1 0 3 12 7 0 3 20 1 12 20 7 12 0 7 3 7 1 12 0 1 3 0 12 0 20 1 3 20 0 1 7 1 12 0 1 3 0 7 3 1 0 12 3 1 0 1 20 12 3 0 1 0 7 1 3 0 12 0 1 3 1 0 1 7 0 1 3 0 7 3 0 3 12 3 7 0 3 1 0 20 7 0 1 12 0 7 0 1 3 0 1 0 12 3 1 3 12 3 7 1 7 20 12 1 20 0 3 1 0 12 3 0 7 12 1 7 3 1 0 1 12 1 0 3 0 1 0 7 12 0 3 1 3 0 7 1 20 0 7 3 0 3 1 3 0 7 1 12 0 1 12 3 0 12 1 20 1 3 12 20 7 12 3 12 0 7 12 0 1 12 3 1 7 12 0 1 7 0 3 1 7 0 1 0 3 20 1 0 7 1 3 1 7 20 7 3 7 0 12 3 1 0 7 0 3 0 1 3 0 12 3 1 3 7 1 3 0 20 7 3 0 12 3 1 0 7 1 0 1 3 0 7 3 0 3 1 0 1 7 1 0 3 1 12 1 0 3 0 7 12 3 1 3 0 12 0 3 0 1 20 12 3 0 3 7 12 1 0 3 0 7 0 3 1 7 3 0 3 12 7 3 12 1 3 7 12 20 7 12 1 20 0 7 3 1 0 3 12 1 0 3 1 0 1 7 0 1 3 12 7 3 0 7 0 1 12 3 20 3 7 1 0 12 3 7 20 12 1 20 7 20 3 12 20 3 20 7 20 0 20 12 20 3 7 12 20 7 1 12 20 3 20 1 20 0 12 20 0 7 12 20 1 7 0 12 3 0 1 3 20 1 7 1 3 0 1 3 12 0 3 7 20 3 12 3 0 1 12 0 7 1 3 1 0 3 1 12 3 1 7 3 1 0 3 12 0 1 20 12 0 7 12 20 1 12 0 3 12 7 1 3 1 0 7 1 3 12 7 1 3 20 1 0 3 12 1 3 20 7 20 12 7 20 3 12 7 3 1 12 1 0 7 0 12 20 3 12 0 7 1 3 1 0 1 7 12 20 7 3 1 0 12 1 7 12 3 1 7 0 3 0 12 3 0 1 3 12 1 3 1 0 3 7 1 3 12 0 1 0 7 1 20 12 3 7 1 12 0 7 12 3 20 12 3 12 1 20 3 7 3 1 7 0 3 1 12 0 3 7 0 12 3 0 1 12 7 0 20 1 12 0 3 12 0 7 3 0 1 3 12 7 1 7 0 1 3 0 7 1 0 1 12 0 7 1 0 3 0 1 0 7 1 3 1 12 3 0 1 12 20 0 7 3 0 1 3 0 12 0 1 0 12 7 0 20 3 1 20 12 7 1 7 3 7 0 3 1 3 12 7 1 7 0 3 1 0 3 0 12 7 3 0 1 7 20 1 0 3 0 12 7 20 3 12 3 7 1 0 7 3 12 20 0 20 1 20 0 7 0 1 7 3 0 1 12 3 0 20 1 7 0 20 0 1 3 0 1 12 1 0 3 0 1 0 12 7 3 0 1 0 3 12 1 20 1 12 1 3 20 7 20 3 0 12 3 0 7 0 1 12 0 1 0 7 1 12 7 20 1 20 0 3 12 20 1 20 7 20 12 1 0 12 3 1 12 1 20 0 20 3 0 20 12 3 0 7 0 1 12 0 1 20 12 0 7 3 1 0 3 12 0 3 7 0 1 0 20 0 3 12 0 7 3 12 20 12 3 0 12 1 3 1 7 12 0 7 3 0 12 0 1 0 12 3 1 7 3 0 1 0 7 0 1 12 7 3 0 7 0 1 20 1 3 12 0 3 0 20 0 7 3 7 12 0 3 0 1 0 7 1 0 3 7 20 3 0 7 1 0 1 12 7 12 0 3 20 1 12 20 7 12 7 0 12 3 1 7 3 12 1 3 0 7 0 20 3 0 3 12 3 0 20 1

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Alphabet {0, 1, 3, 7, 12, 20}

size 6 · diameter 20 · record length 2823 · JSON

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

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