Additive Squares

Alphabet {0, 1, 5, 11, 22}

size 5 · diameter 22 · record length 1997 · JSON

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

Record word (length 1997, by David Renshaw, 2026-08-18)

Display: drawn for the equivalent alphabet translated by -8 (drift removed); downsampled ×2.

0 1 0 11 5 11 1 22 11 0 22 5 11 0 11 5 11 0 1 11 22 5 0 5 22 1 5 11 1 0 22 11 1 22 5 11 0 22 0 11 0 5 22 1 22 5 22 0 11 0 5 1 22 0 22 1 22 5 22 1 22 11 5 22 5 1 22 0 5 1 0 1 22 1 0 5 11 22 0 11 1 0 11 0 5 22 0 22 1 0 5 0 11 22 0 5 1 22 1 5 11 22 1 11 0 1 22 1 11 5 11 1 22 1 11 0 1 0 22 0 11 22 1 22 5 11 22 0 11 1 11 0 22 5 0 22 0 1 0 22 0 11 0 22 1 22 0 11 22 5 0 11 22 11 0 1 22 11 0 11 22 11 0 5 22 5 1 22 11 1 0 1 11 22 5 0 5 11 1 0 5 1 0 1 11 5 11 0 1 11 5 1 5 0 22 5 1 5 11 5 1 5 22 5 0 22 1 0 22 5 11 5 1 5 11 22 11 0 1 0 5 22 11 1 0 1 11 22 11 5 1 22 11 5 22 11 0 5 11 0 11 1 22 5 1 22 11 0 1 22 0 1 0 5 22 0 5 1 11 1 5 22 1 0 1 22 11 22 0 1 0 22 0 5 1 22 0 22 5 0 11 1 22 1 5 22 11 22 5 0 11 22 1 22 5 1 5 11 0 11 5 1 5 22 1 5 0 22 1 11 1 0 22 0 11 22 11 5 11 22 0 1 22 1 11 22 1 0 22 5 11 22 0 22 5 22 1 22 5 22 11 5 11 0 1 11 5 0 5 22 5 1 22 0 5 0 22 11 22 1 5 11 22 0 22 11 22 1 11 0 22 1 5 22 11 0 22 11 22 1 11 22 5 0 5 22 11 22 5 0 22 0 11 22 1 0 22 11 0 22 0 5 0 22 11 22 5 22 11 0 5 11 0 11 1 22 5 0 5 11 22 11 0 5 11 0 1 22 1 5 1 22 0 11 22 0 5 22 1 22 0 11 22 5 11 5 1 22 5 0 5 1 0 11 5 0 11 22 5 1 5 11 0 5 22 5 11 5 0 11 0 22 11 0 5 1 11 1 5 22 5 1 11 0 1 5 1 22 1 0 1 11 1 22 1 0 5 22 11 5 0 5 1 5 22 0 5 11 0 11 1 22 1 11 0 11 1 22 11 22 5 22 11 22 0 22 5 1 5 22 11 22 0 11 5 0 11 0 22 5 11 1 22 5 11 5 1 5 11 22 1 11 0 1 22 5 11 0 22 1 0 11 0 1 5 0 1 11 1 22 11 1 11 0 1 5 22 0 5 1 5 22 0 22 11 22 5 22 0 5 1 0 22 0 1 11 1 22 11 5 0 11 22 11 1 22 0 22 11 0 11 5 0 22 11 0 1 5 11 5 1 5 0 1 11 0 5 22 0 22 11 1 0 11 1 11 5 1 5 0 11 1 0 1 22 11 0 5 1 5 22 11 22 5 0 1 22 1 11 1 0 22 1 0 1 5 1 11 22 5 0 22 0 11 0 1 22 5 1 0 11 5 0 1 0 22 0 5 11 22 11 0 11 1 5 11 0 11 1 0 1 22 1 5 22 1 0 1 11 0 5 0 22 5 11 22 0 1 5 0 11 0 1 5 0 1 11 1 22 1 5 0 11 5 1 0 5 11 22 0 5 1 11 0 11 1 11 5 1 0 5 11 0 5 0 1 5 0 5 22 0 11 1 11 0 11 1 5 1 0 5 0 11 0 1 5 1 0 11 1 5 22 5 1 0 1 11 1 5 1 22 0 22 5 22 11 1 0 5 0 1 0 5 11 22 5 11 0 1 0 5 11 0 11 22 11 0 5 1 11 0 11 22 5 11 5 1 11 0 5 11 22 5 22 0 22 5 11 5 0 11 1 11 22 11 0 1 22 5 1 22 0 22 11 0 5 0 22 5 0 1 22 5 0 5 11 0 11 22 0 5 22 0 1 0 11 1 0 22 11 5 1 11 0 1 5 0 22 1 0 11 0 1 5 0 11 0 22 5 1 5 0 5 22 0 22 1 0 5 1 22 0 1 5 11 5 1 0 1 11 0 22 11 22 5 22 1 5 0 1 11 0 1 22 1 11 22 11 5 1 0 11 0 5 11 0 1 5 1 22 0 22 1 11 22 1 5 0 5 11 22 11 0 22 11 1 22 0 22 1 11 5 0 11 22 11 1 11 22 11 0 11 1 0 1 5 0 11 22 0 22 1 5 22 5 0 11 1 11 0 22 5 0 11 5 0 1 0 11 0 5 11 1 11 22 1 5 1 22 11 1 0 1 5 11 5 22 11 5 0 22 11 0 22 1 11 0 11 22 11 5 22 5 1 5 0 5 11 5 0 1 0 22 5 11 0 11 5 11 0 22 0 1 0 22 5 22 11 5 0 22 1 5 22 0 22 11 22 1 11 22 11 0 22 1 0 5 0 11 5 22 1 22 11 22 1 22 0 22 11 1 0 1 11 1 5 11 1 11 22 0 22 5 11 22 5 22 1 11 22 0 22 5 0 1 11 1 0 5 22 1 0 11 5 1 0 1 5 1 0 11 5 1 0 22 11 5 22 11 22 1 5 22 5 11 22 11 0 1 22 0 1 0 11 22 5 1 5 22 0 1 22 5 11 1 0 22 1 0 1 11 0 22 0 5 22 11 22 1 11 22 0 5 1 11 5 22 11 22 1 11 22 11 0 22 11 1 11 5 0 22 11 1 0 11 0 22 5 1 11 22 5 11 22 0 11 5 0 5 22 5 1 11 0 5 22 0 1 22 1 5 1 22 0 1 11 5 0 22 0 1 0 22 11 22 0 22 11 5 22 5 0 22 1 22 11 5 11 22 11 0 22 11 22 1 11 22 11 0 22 11 22 5 22 0 5 1 22 11 22 5 11 22 11 1 0 1 5 0 5 22 11 22 5 22 0 22 1 0 1 5 22 5 11 22 11 1 22 11 0 11 22 1 11 22 5 1 0 5 1 22 5 11 1 22 1 11 0 1 22 1 0 1 22 5 11 22 5 0 22 11 22 0 22 11 1 11 5 1 0 11 5 0 22 1 5 1 0 1 11 0 5 11 5 22 1 22 5 0 1 0 11 22 1 22 5 22 1 11 0 11 22 11 5 0 1 0 22 1 5 0 1 11 22 5 22 11 22 0 1 0 5 0 11 0 5 22 11 22 1 22 11 22 5 0 5 22 1 11 22 11 0 5 22 1 11 22 0 22 11 22 1 22 5 1 22 11 1 0 11 5 22 0 22 11 0 11 1 5 11 0 5 22 11 22 1 11 1 5 0 1 22 11 1 5 22 5 0 5 1 5 11 22 1 11 5 0 5 1 0 1 11 22 0 5 1 11 1 5 1 22 1 11 22 11 5 11 1 22 0 11 22 11 5 11 1 22 1 11 5 0 5 22 5 1 11 0 22 1 11 0 1 5 11 22 1 22 0 11 22 0 5 0 1 5 0 11 1 0 5 0 22 11 5 22 5 0 22 5 1 0 11 1 0 1 5 11 22 11 0 5 1 5 0 5 11 0 11 1 0 1 5 0 5 11 5 0 5 1 0 5 0 11 0 22 5 22 11 5 11 0 22 1 0 5 0 11 0 1 0 22 5 1 11 1 22 11 22 5 0 5 1 0 11 1 5 11 22 11 5 11 1 5 11 22 1 22 11 22 0 1 11 0 1 5 0 11 5 11 22 1 22 0 11 0 22 0 11 1 5 11 0 1 22 0 11 1 0 1 5 1 0 22 0 1 5 0 22 5 11 0 5 22 1 5 0 22 5 1 22 5 11 1 22 1 0 11 0 1 22 5 22 11 5 1 5 22 5 11 0 11 1 22 5 22 0 22 1 22 11 1 22 0 11 5 0 11 0 22 5 1 22 11 22 5 11 22 0 5 0 11 5 0 1 11 5 11 0 11 5 11 22 11 1 0 22 1 0 1 5 0 1 0 22 5 11 5 0 22 0 5 1 0 1 22 11 22 1 5 1 11 22 0 5 0 22 1 0 22 0 11 22 11 5 22 11 1 11 22 0 22 5 11 5 22 1 5 0 22 11 1 22 0 22 11 22 0 22 5 11 22 0 22 11 22 0 1 22 0 5 11 0 1 22 1 11 1 0 11 22 11 0 11 1 11 5 22 11 22 0 22 11 22 1 0 22 1 11 5 11 0 11 5 1 11 5 22 0 22 11 22 1 0 22 0 11 5 0 5 1 0 1 22 11 22 1 0 5 11 0 22 0 1 11 1 0 22 1 11 5 22 0 5 0 11 0 22 1 0 11 0 5 0 11 0 1 0 5 1 11 1 5 22 1 0 1 22 5 11 1 22 1 5 22 5 0 22 11 1 22 11 22 5 11 1 22 1 5 0 11 0 22 1 5 22 11 0 5 0 22 1 5 0 1 0 11 5 1 22 5 1 5 11 5 1 22 5 22 0 1 22 1 5 22 11 22 0 11 0 1 0 11 0 5 22 5 11

History

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