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

[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.

....