[seqfan] Re: Base sequences like A067581, suggestion: Go Factorial!
franktaw at netscape.net
franktaw at netscape.net
Wed Apr 1 21:05:52 CEST 2009
Oops, that should be
0,2,5,633
Franklin T. Adams-Watters
-----Original Message-----
From: franktaw at netscape.net
I started looking at multiplicative persistence in base factorial -- see
http://www.research.att.com/~njas/sequences/A031346
Unlike the decimal case, there are numbers with unbounded
multiplicative persistence in base factorial -- the product of digits
functions in base factorial takes on every non-negative integer as a
value (infinitely often). It does, however, grow quite slowly: the
smallest number with multiplicative persistence n in base factorial
starts:
0,1,5,633
The next term is <= 443153013, which is (11)1111153311 in base
factorial, with product of digits 693. 693 in turn is 53311 in base
factorial, product of digits is 45, or 1311 in base factorial.
Franklin T. Adams-Watters
P.s. While I generally approve of this idea, by my standards these are
still base sequences and should have the "base" keyword.
-----Original Message-----
From: Antti Karttunen <antti.karttunen at gmail.com>
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.
.....
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