Additive Squares

Word of length 336 over {0, 3, 6, 13}

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

0100200300-100-500 position in word → partial sum

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

0 3 13 6 13 0 13 6 3 6 13 6 0 13 0 3 0 13 0 6 13 0 3 13 6 0 6 13 6 3 6 13 6 0 13 3 0 6 0 3 13 3 0 6 3 6 13 6 0 13 0 3 0 13 0 6 13 0 13 3 6 0 6 13 0 13 3 13 0 13 6 13 3 6 13 6 0 13 3 0 6 3 6 13 6 0 3 0 13 0 3 6 13 3 13 0 3 6 13 6 3 6 0 6 3 6 13 3 0 3 6 0 3 0 13 3 0 3 6 0 6 13 6 3 6 0 6 13 0 13 3 0 13 6 13 0 13 3 0 3 6 0 3 0 13 0 6 0 13 0 3 13 0 13 6 13 0 13 3 13 6 3 13 3 0 6 3 0 13 0 3 6 0 6 13 6 3 6 13 6 0 13 0 3 13 0 13 6 13 3 13 6 13 0 6 13 6 3 0 3 13 6 13 0 6 13 6 3 6 13 6 0 6 3 0 6 0 13 3 6 13 6 0 13 0 3 0 13 0 6 0 3 6 0 6 13 6 3 13 6 13 0 13 3 13 0 13 6 0 13 0 3 0 13 0 6 0 3 6 3 13 0 13 3 13 6 3 0 3 6 3 13 6 3 0 13 0 3 0 6 0 3 13 6 3 0 6 3 6 13 6 3 6 0 6 13 0 13 3 13 6 13 0 13 3 0 6 3 0 13 3 6 13 6 0 6 3 13 0 3 0 6 0 3 0 13 0 6 13 0 13 3 0 6 3 13

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Alphabet {0, 3, 6, 13}

size 4 · diameter 13 · record length 336 · JSON

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

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