[seqfan] Base sequences like A067581, suggestion: Go Factorial!

Antti Karttunen antti.karttunen at gmail.com
Wed Apr 1 17:02:02 CEST 2009

It might also make sense to compute a sequence like


in factorial base( http://www.research.att.com/~njas/sequences/A007623 ),
to make the idea less dependent on any particular arbitrary base.

One should presumably submit two (interlinked) sequences, one showing the
factorial expansion itself, which sequence is by convention, either a)
finite, cutting at the point when digits > 9 will eventually appear, or b)
those digits are represented "in a corrupted was" as ..10.., ..11.., etc.

and the other sequence, corresponding integer values,
where this problem does not occur.

Fac base.    Corresponding integer value
0            0
1            1
20           4
11           3
200         12
111          9
300         18
21           5

etc. (Doodled by hand, please check!)
Both sequences should be tagged as "base".

Now, many such sequences, provided the membership criterion
is chosen with some taste, might actually turn useful,
e.g. when indexing permutations given in some standard
ordering like:

or they might form yet another manifestation
for a well known combinatorial family:
http://www.research.att.com/~njas/sequences/A071156 / A071158

So, if using a "general membership criterion", which doesn't
depend on any previous terms, and the sequence is thus monotone, then check
also whether a derived sequence "number of terms in Axxxxxx with n factorial
digits" yields anything well-known.

And before submitting any such sequence, please, compute it with
a computer, there are enough incorrectly hand-calculated seqs in OEIS



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