Additive Squares

Word of length 6874 over {0, 1, 4, 10, 12, 17}

by David Renshaw, 2026-08-26 · the current record for this alphabet · JSON

Display: drawn for the equivalent alphabet translated by -7 (drift removed); downsampled ×6.

0 17 10 12 10 4 0 17 0 4 12 0 12 1 17 12 4 17 4 1 0 10 0 17 0 1 17 4 0 12 0 1 4 10 4 17 0 17 12 0 1 12 10 12 4 17 1 17 12 17 10 4 17 0 4 17 1 12 17 1 0 4 0 1 10 17 0 1 17 12 17 10 1 12 4 0 1 17 1 0 10 1 4 0 1 10 0 12 0 1 0 4 0 17 4 10 1 17 10 1 0 17 0 10 0 1 0 12 17 4 17 0 17 1 0 12 0 1 0 4 12 17 10 0 1 17 10 4 10 17 0 12 1 4 17 12 17 0 17 10 17 0 1 4 10 17 1 4 17 12 1 17 1 0 12 1 4 1 12 10 17 12 0 4 17 4 1 12 17 12 4 0 1 10 0 1 0 17 1 0 1 12 4 0 10 17 4 1 17 1 0 17 0 4 17 0 1 12 10 17 10 1 17 4 1 17 0 1 0 4 0 17 0 4 10 1 0 4 0 12 1 0 10 0 1 0 10 4 0 1 17 0 1 0 12 1 10 0 12 4 0 1 0 12 4 17 0 1 10 0 17 1 12 4 12 17 4 0 17 4 10 17 12 4 0 12 0 17 0 4 0 12 0 1 0 17 0 4 0 17 0 1 17 1 4 0 17 12 1 0 12 17 0 4 17 10 4 0 17 12 1 4 17 1 10 0 10 12 17 0 17 1 0 12 0 1 17 0 1 10 4 1 0 17 1 17 10 17 4 0 4 17 12 17 1 0 1 10 4 0 17 1 10 17 0 17 4 10 17 4 12 0 12 17 10 12 17 4 17 0 17 4 17 1 12 17 0 1 0 17 0 10 12 4 0 1 10 0 10 17 0 17 1 12 17 4 1 0 1 17 10 12 17 10 17 4 1 12 17 10 1 12 17 1 0 12 0 1 0 17 1 0 4 0 1 17 12 0 1 0 17 1 0 10 4 0 1 0 17 10 17 4 17 1 0 1 10 17 0 10 1 0 1 12 0 1 17 0 1 0 4 0 12 4 0 4 1 0 1 10 0 17 0 12 1 17 0 4 1 10 4 17 0 1 17 0 17 12 0 17 4 17 0 12 1 0 1 17 0 1 10 1 0 4 0 17 12 0 17 1 17 0 17 12 17 0 17 10 17 0 1 0 17 0 1 12 0 1 17 1 4 10 17 4 1 0 4 12 1 0 1 17 0 1 4 17 4 0 4 1 17 12 4 1 0 10 17 0 12 1 4 17 1 0 10 17 12 4 0 1 4 10 17 1 0 4 0 1 0 17 0 1 0 12 0 1 0 4 0 1 0 17 1 4 0 12 1 0 1 17 0 1 4 0 1 0 10 1 12 10 0 17 4 0 1 17 4 10 0 1 17 0 12 4 10 4 17 12 1 4 17 1 0 4 12 0 1 0 17 1 0 10 4 0 1 0 17 0 12 0 17 1 4 17 0 1 17 10 1 17 0 4 10 12 4 1 17 0 17 4 1 17 0 1 17 12 10 4 0 1 0 4 17 0 12 1 0 1 4 17 0 17 4 17 1 4 17 0 17 4 10 17 1 4 0 10 17 12 0 17 4 17 0 10 0 1 17 0 4 1 12 17 12 4 12 10 0 4 17 0 10 17 10 1 0 4 1 17 0 1 0 4 1 0 10 0 12 1 17 1 0 1 10 4 17 1 0 17 1 4 17 12 0 17 1 4 17 1 17 0 1 4 1 0 10 1 0 1 4 0 1 17 0 4 0 10 0 1 0 12 0 10 0 17 12 0 10 0 1 4 0 1 12 1 17 12 17 0 17 4 17 0 17 1 0 17 0 4 17 12 1 17 10 1 17 0 4 0 17 1 0 10 0 1 12 0 1 17 0 4 17 0 12 0 17 0 12 1 12 17 12 4 1 17 1 0 17 4 0 17 12 0 4 0 12 0 1 17 0 1 0 4 17 1 4 12 17 4 17 1 0 17 12 17 10 17 4 17 12 17 0 17 1 12 0 17 10 12 4 1 17 12 0 17 1 10 4 0 17 1 17 0 10 0 1 0 17 12 4 17 1 4 10 1 12 0 17 4 1 0 1 4 1 10 0 1 10 17 4 17 1 17 12 0 1 12 4 0 12 0 1 17 1 4 12 1 0 17 12 17 1 10 0 4 17 1 17 12 17 1 0 17 1 4 17 1 12 1 17 4 1 17 1 10 1 4 1 17 0 17 1 4 17 12 17 0 1 10 0 4 1 0 4 17 0 1 0 17 12 1 12 4 10 1 0 17 1 0 4 10 1 0 1 12 0 1 0 4 17 1 0 12 1 4 17 1 12 0 17 0 4 17 1 0 1 12 1 10 12 17 1 12 17 4 1 17 12 1 12 10 4 0 17 4 0 12 0 17 12 0 1 4 0 17 12 1 0 12 10 0 4 1 4 17 0 1 0 10 4 1 0 1 4 12 4 0 1 4 17 12 17 0 17 12 1 0 4 1 0 17 0 12 10 12 17 1 4 1 17 1 10 4 12 17 12 1 12 0 1 17 12 17 0 17 4 17 12 0 17 1 0 17 0 10 12 0 1 17 12 0 1 0 17 0 4 0 17 0 12 17 0 17 1 0 17 12 17 0 17 12 10 17 12 17 0 12 17 12 1 17 0 17 12 17 1 17 10 17 0 17 1 12 1 0 17 10 1 4 1 0 17 0 1 4 0 4 17 10 1 17 4 1 17 1 10 4 10 0 17 10 17 4 12 17 12 1 17 12 0 4 17 0 4 0 1 17 0 1 0 10 0 1 17 1 0 12 0 1 4 1 0 1 12 0 12 17 4 1 17 10 1 4 17 4 0 17 1 17 12 17 0 1 17 0 12 10 0 1 4 0 10 12 0 10 1 17 1 0 17 1 17 10 17 0 4 17 12 17 1 10 17 4 0 17 1 17 0 17 4 0 1 12 17 0 17 1 4 10 0 1 17 0 1 12 0 4 17 4 1 17 0 17 12 17 1 17 0 17 1 17 4 1 17 1 12 10 12 17 12 1 12 17 0 17 12 17 4 12 17 1 17 0 17 12 17 4 17 1 17 10 17 12 1 17 12 0 1 12 10 17 0 17 10 17 1 12 0 4 0 17 12 0 17 1 0 12 1 0 10 17 0 12 17 10 12 1 0 17 10 4 17 0 1 10 17 1 17 4 1 0 4 1 12 0 12 17 0 4 0 1 17 0 4 17 4 1 4 0 1 0 10 1 4 12 1 12 0 17 1 12 1 10 17 12 10 17 4 17 12 17 4 0 17 1 17 12 17 0 17 12 17 10 12 4 0 17 0 1 0 4 1 17 4 17 12 1 12 17 4 12 10 17 12 0 17 12 10 17 10 1 17 12 1 17 1 4 12 0 17 4 0 12 0 1 17 0 12 4 12 17 0 1 0 12 1 0 4 1 0 1 17 1 0 4 0 17 0 4 0 12 4 17 1 12 1 4 1 0 10 1 4 17 0 12 17 1 17 12 17 1 4 12 1 0 4 17 4 0 1 0 17 1 12 17 1 4 17 1 17 0 1 10 0 17 12 17 4 10 17 4 17 12 17 0 12 4 1 17 10 4 0 4 17 0 17 12 4 1 0 17 4 12 17 0 10 0 17 1 0 1 4 17 4 1 12 4 17 4 1 17 4 17 0 4 17 1 4 17 4 10 0 1 17 0 1 0 12 17 1 0 17 0 4 0 1 0 10 4 0 1 0 17 10 17 0 12 0 4 1 12 0 10 1 4 0 1 17 0 1 4 1 0 1 12 1 4 1 17 4 1 0 12 0 4 1 0 4 17 0 17 1 0 17 0 12 17 1 17 4 0 17 4 1 17 1 0 17 1 12 1 4 17 0 17 4 1 4 17 0 12 17 0 10 0 1 4 1 0 1 12 4 1 17 4 1 0 17 4 17 1 4 12 17 10 17 0 17 1 17 0 17 10 17 12 17 1 0 17 4 17 1 17 10 4 12 17 1 0 4 1 10 12 1 17 1 0 17 12 10 12 0 4 12 4 17 10 12 17 12 1 17 12 17 10 4 17 12 17 10 12 17 0 1 0 17 12 0 12 10 17 12 1 17 1 0 17 4 1 17 12 4 1 17 1 0 10 1 0 4 0 17 0 1 0 17 0 12 0 1 12 17 1 17 10 1 12 4 10 1 10 0 12 0 17 0 4 0 10 0 12 0 1 0 12 4 1 0 1 4 17 0 1 0 10 1 0 4 0 17 1 12 4 17 1 10 0 1 0 17 1 0 1 12 1 17 1 4 17 4 12 0 17 0 1 17 0 4 10 1 0 17 1 0 12 1 4 0 1 10 1 12 17 0 12 1 17 1 0 1 17 4 0 17 10 4 1 10 17 12 17 0 17 1 0 17 10 0 17 12 17 0 17 10 4 17 0 17 12 17 10 17 0 10 0 1 17 0 17 12 17 10 0 1 4 0 4 10 0 17 1 17 4 17 10 17 4 1 17 0 1 4 0 12 0 4 0 10 1 17 1 0 17 4 17 0 10 12 1 10 17 12 1 12 0 4 10 0 1 4 0 17 0 1 0 10 0 17 4 1 17 0 1 10 17 10 4 1 4 0 1 17 0 4 12 0 1 17 0 10 1 17 4 0 1 4 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1 0 17 4 17 1 4 17 12 1 0 12 4 1 4 17 4 0 1 17 1 12 1 0 12 1 12 17 12 0 17 4 0 1 0 17 12 0 17 4 17 0 17 1 12 17 0 17 1 0 1 12 0 17 10 1 0 12 0 4 1 17 10 17 1 0 17 1 4 1 0 1 17 1 0 1 10 17 0 17 1 0 17 4 17 0 17 10 0 17 1 0 12 0 17 0 1 0 17 0 4 1 0 17 0 1 10 12 4 0 4 1 0 17 0 1 4 0 12 1 0 1 4 1 0 1 17 4 0 4 10 0 4 1 17 4 0 17 4 17 10 0 1 17 0 1 0 10 0 4 1 0 17 1 0 4 12 4 10 4 1 0 1 12 0 17 1 17 4 17 10 17 1 17 0 17 4 12 1 17 0 1 4 1 0 1 4 10 1 0 1 4 0 1 17 10 12 1 17 0 17 4 17 0 17 1 0 17 0 10 1 4 1 0 17 10 1 4 10 17 1 17 0 1 17 12 17 10 12 1 17 0 1 10 12 17 10 17 1 4 17 0 12 1 0 17 4 17 0 1 12 1 4 0 1 4 1 10 17 0 17 4 0 10 0 17 1 12 17 4 17 0 12 0 4 17 10 17 1 0 1 4 0 1 0 10 4 0 4 12 0 1 10 12 1 17 10 0 17 0 1 4 1 17 12 17 10 0 1 17 12 1 0 17 0 1 0 17 4 17 12 17 1 17 4 0 10 4 1 12 17 1 17 0 12 17 12 10 12 1 17 10 17 12 17 10 0 12 17 10 17 1 10 0 4 10 1 17 4 12 4 17 1 0 1 4 17 4 12 10 1 12 0 1 12 17 0 1 0 17 0 1 4 17 1 17 0 1 0 4 10 17 12 17 0 17 12 17 10 17 0 1 17 4 17 12 0 4 1 10 1 17 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Alphabet {0, 1, 4, 10, 12, 17}

size 6 · diameter 17 · record length 6874 · JSON

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

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Record history

• 6874 (was 71) — David Renshaw, 2026-08-26
• 71 (first) — Bryna Kra, 2026-08-26

Comments

• David Renshaw · 2026-08-26 17:24 UTC

  Generalized the public lockstep sibling-recycling population search to the sparse alphabet {0,1,4,10,12,17}. Starting from word 310 (length 71), a short benchmark reached 1000, followed by a 15-minute adaptive campaign of 18 forward/reversed population branches (W=4096 and 8192, beta=0.0-5.0, rewrite depths 20-2200). I repeatedly forked the leading checkpoint and also tried exact SMT suffix repair, randomized mobility DFS, and speculative self/reversal splices. The best branch reached 6874. Independently verified all 11,812,969 start/block-length pairs before submission.

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