Additive Squares

Word of length 320 over {0, 4, 5, 12}

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

0100200300050 position in word → partial sum

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

0 12 4 0 4 5 12 0 5 4 0 5 12 0 4 12 4 5 12 5 0 12 4 12 5 0 12 0 4 0 5 0 12 0 4 12 4 5 4 0 5 0 12 5 0 5 4 5 12 4 5 4 0 4 12 0 12 5 12 4 5 4 0 12 4 12 5 12 4 12 0 12 5 4 5 0 12 0 5 4 0 4 12 4 5 0 12 0 5 0 4 5 12 5 4 5 0 5 4 12 5 12 0 12 5 4 12 4 0 4 5 0 12 5 12 4 5 0 12 0 4 0 5 0 4 0 12 4 5 4 0 5 0 12 0 5 0 4 5 0 5 12 5 4 5 0 4 0 12 4 12 5 12 4 0 4 5 4 12 4 5 4 0 5 0 12 0 4 0 5 4 0 4 12 4 5 4 12 4 0 12 4 12 5 12 4 12 0 12 5 0 5 4 0 4 12 0 5 0 4 5 0 5 12 5 4 12 4 0 4 12 4 5 12 4 12 0 5 4 5 12 4 12 0 12 4 12 5 12 0 5 12 5 4 12 4 0 5 4 5 12 5 0 12 5 12 4 12 0 4 0 5 4 0 4 12 4 5 12 5 0 5 4 0 5 0 12 0 4 0 5 4 0 4 12 4 5 12 4 12 0 12 4 12 5 12 0 5 4 5 0 12 0 4 0 12 5 12 4 12 0 4 5 0 12 5 0 5 4 5 0 5 12 0 12 4 12 5 12 0

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Alphabet {0, 4, 5, 12}

size 4 · diameter 12 · record length 320 · JSON

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

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