Additive Squares

Word of length 254 over {0, 1, 2, 4, 5}

by David Renshaw, 2026-08-19 · the current record for this alphabet · JSON

050100150200250050100 position in word → partial sum

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

1 0 1 4 1 2 0 5 4 2 5 4 1 5 4 0 1 0 5 1 5 2 1 2 0 2 1 2 5 1 4 5 4 2 5 0 1 0 4 1 0 2 0 1 0 4 1 5 1 2 0 1 4 5 4 1 4 0 1 0 2 4 5 0 2 4 2 5 4 1 0 4 2 5 4 0 5 4 5 2 5 4 5 1 4 5 4 0 2 5 4 1 0 2 1 5 0 5 4 5 2 5 4 1 2 5 0 4 2 5 0 2 0 1 2 5 2 0 4 1 4 5 2 4 5 0 4 0 2 1 2 5 0 4 0 2 0 1 2 0 2 5 0 1 0 2 0 1 0 4 0 1 0 2 0 1 5 2 1 0 4 0 1 5 4 0 1 4 2 1 0 2 1 2 5 0 4 5 4 2 5 2 1 0 2 5 1 2 5 4 5 0 5 4 5 2 5 4 5 1 2 0 5 1 5 4 5 1 5 0 1 0 2 1 2 5 2 1 0 1 2 4 0 1 0 2 1 2 5 4 2 5 2 0 1 5 2 5 4 5 2 1 2 5 4 2 5 2 0 1 0 5 1 0

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Alphabet {0, 1, 2, 4, 5}

size 5 · diameter 5 · record length 254 · JSON

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

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