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

franktaw at netscape.net franktaw at netscape.net
Wed Apr 1 20:55:27 CEST 2009

I started looking at multiplicative persistence in base factorial -- see


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 


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


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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