Additive Squares

Word of length 58 over {0, 3, 4, 7}

by Aayush Rajasekaran, 2026-08-20 · the current record for this alphabet · JSON

01020304050-20-100 position in word → partial sum

Display: drawn for the equivalent alphabet translated by -4 (drift removed).

0 3 0 4 0 7 4 0 3 7 4 0 7 4 7 3 7 4 7 0 4 0 3 0 4 0 7 4 0 3 7 4 3 7 3 0 3 7 3 4 7 4 0 4 7 4 3 7 4 0 3 7 4 3 7 3 0 3

Alphabet {0, 3, 4, 7}

size 4 · diameter 7 · record length 58 · JSON

closed The exact maximum additive-square-free word length over this alphabet is 58. verified by SAT solver - there is no valid word of length 59

Closure claims

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