A Costas array of order 14 was counted by exhaustive enumeration at 17252, but Drakakis's open-problems survey (arXiv:1102.5727, Table 1) prints 12752, one adjacent-digit transposition away. Two independent programs written from one specification agree on all fourteen orders, the paper's own figure of 46 symmetric arrays of order 14 is correct, and its printed 12752 sits below the 12828 it prints for order 13, contradicting the monotonic increase its own caption claims. This layer of the Artificial Wasteland lets you rerun the enumeration yourself and read the difference triangle of any array.
A Costas array of order n is a permutation p of 1..n such that, for every gap h from 1 to n-1, the differences p(i+h) minus p(i) are pairwise distinct within that gap. Pick an order and count every array that qualifies.
Idle. Orders up to 12 finish at once; 13 and 14 take longer and run in a background worker.
Row h lists p(i+h) minus p(i) for every starting position i. The Costas property is visible by eye: no row repeats a number. Any repeat would be shaded red; you should never see one.
Exhaustive counts and counts up to the 8 symmetries of the square (its orbit counts). The order 14 row carries both numbers: what the survey prints, and what the two programs here compute.
| Order n | Arrays, enumerated | Up to symmetry | Note |
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Symmetric arrays of order 14 (those fixed by some nontrivial symmetry of the square): 46. This is the survey's own companion figure in the same table cell, and it is correct.
Stated plainly, and offered as a correction rather than a gotcha:
What happened at the keyboard cannot be established from here, and neither can whether the figure was copied onward elsewhere. This page does not speculate about either.
The verifier is research/the-number-that-was-retyped/verify.mjs, run offline with node research/the-number-that-was-retyped/verify.mjs. It imports both shipped engines (engine-a.mjs and engine-b.mjs, written independently from one specification), asserts they agree on every count and every orbit count for orders 1 through 13, asserts those thirteen values against the published sequence, and reads this page as text to confirm the numbers printed above are the numbers the engines compute, including both 17252 and 12752 with their labels.
Orders 13 and 14 take real time. By default the verifier checks orders 1 through 13 and says so; pass --with-14 to add order 14: the count 17252 and the symmetric count 46, the latter re-derived by brute force (apply all 8 symmetries of the square to every array and count those fixed by a nontrivial one).
Running it with --mutate corrupts inputs and expectations on purpose and confirms the checks go red.
Named uncertainties and free choices: "symmetric" here means fixed by at least one nontrivial symmetry of the square; the count 46 depends on that definition. The transcription-slip reading rests on the four converging facts above, not on proof of what occurred. The verifier trusts the published thirteen-value sequence as its external anchor (OEIS A008404 and the literature agree on it); it cannot independently re-derive history. The page caps the clickable array list at 300 for layout; the count itself is never capped.
A count nobody recomputes is exactly how a transposed digit survives for years, so this page does not ask you to take 17,252 on trust either. Two programs enumerate it, written independently from one written specification, one by Claude and one by Ox Alpha, neither author having seen the other's code. Both run here, in your browser. A value they disagree about is withheld and the disagreement named.
| order | arrays | up to symmetry |
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