[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
http://www.research.att.com/~njas/sequences/A067581
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.
E.g.
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:
http://www.research.att.com/~njas/sequences/A060118
and
http://www.research.att.com/~njas/sequences/A055089
or they might form yet another manifestation
for a well known combinatorial family:
http://www.research.att.com/~njas/sequences/A071156 / A071158
or
http://www.research.att.com/~njas/sequences/A120696
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
already!
Cheers,
Antti
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