Additive Squares

Word of length 1506 over {0, 1, 4, 9, 18}

by David Renshaw, 2026-08-18 · JSON

This is a historical record from 2026-08-18, superseded on 2026-08-20 by length 1966jump to the current record (2240).

0500100015000200400600 position in word → partial sum

Display: drawn for the equivalent alphabet translated by -6 (drift removed); downsampled ×2.

0 1 0 9 4 9 1 18 9 0 18 4 9 0 9 4 9 0 1 9 18 4 0 4 18 1 4 9 1 0 18 9 1 0 4 9 4 1 18 4 18 0 1 9 0 9 4 1 0 4 0 9 0 18 0 4 0 18 1 0 1 9 4 18 4 9 1 0 9 0 4 9 4 1 0 4 9 18 4 18 1 0 4 18 9 18 0 18 9 4 0 4 9 1 9 4 18 0 18 1 0 1 9 1 18 0 18 4 18 0 9 4 1 4 0 1 18 4 0 18 0 1 18 1 4 18 9 18 4 18 9 0 9 18 4 18 9 1 4 18 4 9 0 4 18 9 4 18 4 1 9 4 18 9 18 0 1 18 1 9 1 0 1 9 4 9 0 9 1 0 4 18 9 18 4 0 4 9 1 4 0 4 9 18 4 1 0 9 4 9 0 9 1 0 1 4 1 9 1 0 1 18 1 0 1 4 0 9 0 4 18 9 0 18 0 1 9 4 18 0 4 1 18 1 0 1 18 1 9 0 1 4 0 1 18 0 1 9 4 18 9 0 9 18 1 4 1 0 18 4 18 1 18 4 9 4 18 0 9 18 1 4 1 9 4 9 0 4 1 9 18 1 0 4 1 4 18 1 4 9 18 1 9 1 4 0 18 0 9 1 0 1 4 0 1 18 1 9 4 1 0 18 4 1 4 0 4 9 4 0 4 18 1 9 18 4 9 18 9 1 0 4 1 4 9 1 0 18 9 0 4 9 18 1 4 9 18 9 1 9 18 4 1 18 9 18 0 9 18 9 1 18 4 18 9 18 4 18 0 18 4 18 9 4 0 4 1 18 0 1 4 9 0 18 4 9 0 9 18 0 1 18 9 18 4 0 9 0 4 0 1 18 9 1 4 0 4 9 1 9 0 18 4 18 1 4 1 9 18 4 0 1 0 18 0 9 18 1 4 0 9 4 9 18 4 18 0 4 9 4 18 4 1 4 9 18 9 1 9 18 9 0 1 9 18 1 4 18 9 4 0 18 9 1 18 9 4 18 9 1 18 9 18 0 18 9 18 1 18 9 4 18 9 18 1 0 1 9 4 18 9 18 1 0 9 18 1 18 9 18 1 0 4 18 0 9 18 9 4 18 0 9 18 4 18 1 9 0 1 18 4 1 18 9 0 18 0 1 4 18 1 4 9 18 4 0 18 4 1 9 0 18 0 1 4 0 18 0 4 9 4 0 4 1 18 4 9 18 4 1 4 18 9 4 0 4 9 1 18 9 18 0 1 9 18 0 9 4 9 0 18 1 18 4 18 9 4 1 0 9 18 9 1 4 0 1 9 0 9 4 9 1 0 1 18 1 0 1 4 9 1 0 18 4 0 9 1 4 1 0 4 0 9 18 0 18 1 4 18 4 9 4 1 0 1 18 9 0 9 1 9 4 0 1 4 9 1 9 0 9 1 9 4 9 1 9 18 4 18 0 18 4 18 1 4 0 18 9 4 0 4 1 4 0 9 4 18 4 9 4 18 1 9 0 18 0 1 18 0 9 18 4 18 9 0 18 9 18 1 18 9 0 9 18 9 1 18 9 4 18 1 18 0 1 9 0 18 0 4 9 1 18 0 4 1 18 0 18 1 18 9 1 0 1 18 0 18 4 0 9 0 4 1 9 1 18 4 1 18 0 4 9 18 4 0 1 0 18 4 0 9 0 18 1 9 4 1 9 1 18 9 0 18 0 1 18 9 4 0 4 1 18 0 18 1 18 4 18 9 18 4 1 18 0 9 0 18 0 1 9 4 1 9 1 18 1 0 9 1 4 18 9 18 4 0 9 1 4 1 0 18 1 4 0 1 4 9 18 9 1 0 1 4 1 0 9 4 0 18 1 4 0 1 0 18 1 0 9 0 18 0 9 0 4 18 4 9 18 9 0 18 1 0 18 0 4 18 4 9 1 18 0 1 9 1 0 18 0 9 1 9 4 1 4 0 4 18 0 1 4 9 18 9 1 9 4 0 1 4 0 4 9 4 0 4 1 4 18 1 9 4 0 1 0 18 1 18 9 1 18 0 9 0 18 0 9 4 0 4 1 18 1 4 9 4 1 0 18 4 1 0 1 9 0 1 18 4 0 1 0 4 0 9 0 4 0 18 0 4 1 4 18 1 18 9 4 1 4 9 0 9 1 9 4 0 1 18 0 1 0 9 1 0 1 4 9 4 1 4 9 18 4 0 1 0 9 4 0 1 18 1 0 1 9 1 4 1 0 1 4 1 18 1 0 4 1 0 1 9 1 0 4 18 0 4 1 0 1 9 0 1 0 4 9 0 18 9 0 4 0 9 18 0 18 4 0 4 1 9 18 0 1 0 4 1 9 0 9 1 18 9 18 0 4 18 0 18 1 4 18 4 9 1 4 0 1 9 0 9 18 1 0 1 9 4 0 1 0 4 0 1 18 0 1 4 1 18 1 0 1 9 1 4 1 0 4 1 18 1 0 1 4 1 0 9 18 0 9 4 0 1 9 0 18 0 4 18 1 9 1 0 4 18 0 1 4 9 4 18 1 9 18 1 0 4 0 18 9 18 0 4 18 9 4 18 4 1 9 4 1 0 1 18 1 0 1 9 0 18 0 1 4 0 1 9 18 1 0 9 0 18 0 9 1 4 1 0 9 18 9 4 9 0 4 9 1 0 18 4 0 4 9 4 1 0 1 18 0 1 9 4 18 0 18 9 0 18 0 1 9 1 4 0 4 18 9 18 4 18 0 18 1 9 18 4 0 9 18 4 1 9 0 18 1 18 0 18 4 1 4 18 4 0 18 1 18 0 18 1 9 18 1 18 0 18 1 4 18 0 18 1 0 18 9 18 1 4 0 9 0 18 4 0 18 9 18 4 18 9 1 0 18 1 9 1 0 4 18 9 18 4 1 18 4 0 1 9 4 0 18 4 0 4 1 18 4 18 9 1 4 1 18 1 9 4 9 0 9 4 1 18 4 1 9 1 4 0 18 1 18 0 9 1 18 1 4 0 1 18 4 1 4 9 0 1 0 9 0 1 4 9 4 1 4 9 0 18 0 9 4 9 0 18 0 1 0 18 9 18 4 1 4 9 4 0 18 4 9 1 0 18 1 4 1 9 0 9 18 9 0 4 0 1 0 9 4 0 9 1 9 18 9 1 9 0 9 1 4 18 4 0 9 1 9 4 9 18 0 9 18 1 9 18 0 4 9 4 18 4 1 18 4 18 0 18 9 18 4 18 1 18 4 18 9 18 4 1 4 9 1 9 0 9 18 9 1 18 4 1 18 9 0 18 0 1 4 0 1 9 18 4 18 9 18 0 4 1 4 0 9 1 4 18 9 4 1 4 9 4 1 0 1 9 0 18 9 1 18 1 0 1 4 0 1 9 4

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Alphabet {0, 1, 4, 9, 18}

size 5 · diameter 18 · record length 2240 · JSON

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

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