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[14] (2, 1, 3, 6, 4, 5, 10, 8, 7, 14, 12, 9, 11, 0, 13) (*)

[16](11, 1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 7, 14, 16, 13, 0, 15) (*)

(*) Found by Bubbler (see link).

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From ----_Peter Luschny_, Aug 05 2024: (Start)

User Bubbler, Comments and solution to challenge : <a href="https://codegolf.stackexchange.com/q/274665/123995">Lexicographically earliest permutation of the initial segment of nonnegative integers subject to divisibility constraints</a>, code golf, StackExchange.

From ----: (Start)

Since we On StackExchange (see link), user Bubbler found by exhaustive analysis for n < 29 that only n <= 14 and n = 16 have no proof a solution. Bubbler also states that such a permutation exists for all n, we define "since the escape clause 4th Ramanujan prime is 29, there are at least four primes that are greater than n/2 (i.e., prime factors that appear only once) when n >= 29 but there are only 3 positions that all terms such primes can go (both sides of 0 and the row are equal to 0 if it does not existfirst element), which proves that there is no solution when n >= 29."

We set all terms of row 15 equal to 0 by convention to make the sequence finite and full. (End)

User Bubbler, Comments and solution to challenge <a href="https://codegolf.stackexchange.com/q/274665/123995">Lexicographically earliest permutation of the initial segment of nonnegative integers subject to divisibility constraints</a>, code golf, StackExchange.

[10] (1, 2, 4, 3, 9, 5, 10, 8, 7, 0, 6)

[11] (6, 1, 2, 4, 3, 9, 5, 10, 8, 7, 0, 11)

[12] (1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 7, 0, 11)

[13] (7, 1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 11, 0, 13)

[14] (2, 1, 3, 6, 4, 5, 10, 8, 7, 14, 12, 9, 11, 0, 13)

[15] (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

[16](11, 1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 7, 14, 16, 13, 0, 15)

nonn,tabl,new,fini,full

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[ 9] (3, 1, 2, 4, 5, 0, 7, 8, 6, 9)

[10] (1, 2, 4, 3, 9, 5, 10, 8, 7, 0, 6)

[11] (6, 1, 2, 4, 3, 9, 5, 10, 8, 7, 0, 11)

[12] (1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 7, 0, 11)

[13] (7, 1, 2, 4, 3, 6, 8, 5, 10, 12, 9, 11, 0, 13)

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