Additive Squares

Word of length 407 over {0, 3, 5, 13}

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

0100200300400050100 position in word → partial sum

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

0 3 5 13 5 3 0 3 13 3 0 5 13 0 5 0 3 5 3 13 5 0 5 13 3 13 5 13 0 3 0 5 0 13 3 5 3 13 3 0 3 13 3 5 13 0 13 3 0 13 0 5 0 3 0 13 3 5 3 0 5 0 13 0 5 0 3 5 0 13 5 13 3 13 0 13 5 13 3 5 3 0 3 13 3 0 3 5 0 3 13 0 5 3 5 13 5 0 5 13 5 3 13 0 13 3 13 5 13 3 0 5 0 13 0 3 13 3 5 3 13 3 0 13 3 13 5 13 0 13 5 13 3 5 13 5 0 5 3 5 13 3 13 0 13 5 13 3 13 0 3 5 3 0 13 0 5 13 5 3 5 0 5 13 0 5 0 3 0 13 3 0 3 5 3 13 3 0 13 0 5 0 13 3 0 13 0 5 13 5 3 0 5 13 0 13 3 13 5 13 3 13 0 3 13 3 5 0 5 13 0 13 3 0 13 0 5 3 0 3 13 3 5 3 0 3 13 0 5 0 13 3 13 5 0 5 3 0 5 0 13 0 3 0 5 3 0 3 13 3 0 3 5 0 5 13 3 0 3 13 3 5 3 13 3 0 13 5 13 3 0 3 5 3 0 13 0 3 0 5 3 5 13 5 0 13 5 13 3 0 13 3 5 3 0 5 3 5 13 3 0 3 13 3 5 13 0 13 5 13 3 13 5 0 13 0 3 13 0 13 5 13 3 5 0 5 13 0 5 0 3 5 0 5 13 3 5 3 0 3 13 3 5 13 0 13 5 13 3 13 5 0 13 0 3 0 5 3 5 13 0 13 5 3 13 0 3 13 3 5 3 13 3 0 3 5 0 3 0 13 0 3 0 5 0 13 5 3 13 0 3 0 5 3 0 3 13 3 5 13 5 0 13 3 13 5 13

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Alphabet {0, 3, 5, 13}

size 4 · diameter 13 · record length 407 · JSON

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

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