Additive Squares

Word of length 686 over {0, 1, 2, 4, 8}

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

02004006000100200 position in word → partial sum

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

0 2 4 0 1 8 2 4 1 0 4 8 1 4 2 0 2 8 4 8 2 8 0 8 1 2 1 0 8 0 1 4 1 0 2 8 0 2 0 1 8 4 2 0 8 2 8 4 1 2 8 2 1 0 4 0 2 4 0 1 4 8 4 1 0 1 2 1 0 4 8 0 2 0 1 2 4 8 2 1 4 0 1 2 8 0 8 4 8 2 1 2 4 8 0 8 2 4 8 1 8 4 8 0 1 8 0 8 2 1 8 4 8 1 0 1 4 8 4 0 2 1 8 0 1 2 0 1 0 4 1 2 0 8 4 0 4 1 4 8 4 2 4 0 2 0 8 2 0 1 8 2 8 1 4 8 1 8 2 8 1 8 0 8 1 8 4 8 1 8 0 1 4 2 8 0 2 4 8 4 0 4 8 2 8 0 8 1 8 2 8 0 2 1 0 1 4 0 4 8 1 2 4 8 0 4 1 8 4 8 0 4 8 4 2 1 0 1 2 8 2 0 8 2 8 4 8 0 8 4 8 1 8 4 2 0 2 4 8 1 2 8 1 8 4 8 0 8 2 8 4 8 1 8 4 8 0 4 8 1 2 4 8 0 8 2 8 4 2 1 4 1 8 0 1 2 8 4 8 2 8 0 8 1 2 0 1 0 4 0 8 4 8 1 2 8 0 2 4 2 8 1 8 4 8 2 8 0 8 4 8 1 2 8 1 8 0 8 1 4 8 0 2 1 0 8 0 4 8 4 2 0 8 0 1 2 0 1 8 4 2 0 4 1 2 0 1 0 4 8 1 8 2 1 4 1 8 4 0 8 4 8 2 8 0 8 4 8 1 8 2 1 4 2 1 0 2 8 1 8 4 8 0 1 2 8 0 2 4 2 0 2 8 0 1 0 2 0 4 8 0 2 1 4 1 2 1 0 1 2 1 8 1 4 8 0 2 0 4 0 8 4 8 2 8 0 4 1 4 8 0 2 4 1 2 1 8 2 0 1 4 2 0 2 1 0 8 0 1 2 0 4 1 0 2 0 1 0 2 8 2 4 2 0 8 4 0 4 1 8 4 2 0 2 8 4 8 0 2 0 4 0 2 0 1 0 4 0 8 0 1 0 2 4 0 4 1 8 2 1 8 4 8 0 4 1 8 4 8 0 8 4 8 2 1 0 8 4 0 1 0 4 0 2 1 4 8 0 8 4 8 2 4 2 0 8 4 8 2 4 8 1 8 2 8 4 8 0 4 0 2 8 0 8 4 0 8 1 0 2 0 8 0 4 8 0 8 2 4 8 1 0 1 4 0 4 8 4 0 1 2 0 4 8 0 4 0 1 0 8 0 1 0 4 1 0 2 1 4 0 4 1 4 2 4 8 4 1 2 1 0 1 8 4 2 8 4 1 0 8 4 1 8 4 8 0 8 4 2 8 1 8 0 8 2 4 2 8 2 0 1 4 8 4 0 2 4 0 1 0 4 0 1 8 0 2 4 2 8 4 8 1 8 4 0 8 4 2 8 1 4 8 1 0 2 4 2 0 2 4 8 0 8 1 0 4

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Alphabet {0, 1, 2, 4, 8}

size 5 · diameter 8 · record length 686 · JSON

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

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