Specifically for coldtortuga

[pmb]

A variation on a previous theme:

Base	Number	Number in Base 10
2	12	1
3	23	2
4	3124	54
5	4135	108
6	4126	152
7	651427	16200
8	76251348	2042460
9	82715369	4416720
10	986731210	9867312
Still churning - these O(nn) algorithms really soak up the CPU time... (I later hit Ctrl-C, so all numbers after this point are from coldtortuga)
11	A9876241311	2334364200
12	B935217612	421877610
13	CBA9584721313	1779700673520

Comments

[coldtortuga.livejournal.com]

My "heuristic" approach pretty much follows the algorithm described by pmb, which is (as ya'll surmise) O(n!).

In base n, start with the set of usable digits D={1, ..., n-1}. For each non-empty subset d of D (in Gray-code order, 'cause I already had a Gray-code subset generator), I find and test all the permutations of d (in the order given by Heaps' algorithm, 'cause I already had Heaps coded up). Gray-code + Heaps' algo does not the most efficient search-order make, but it's not too shabby.

The number of candidates to test in base n is given by A007526 which grows like e*n!