[seqfan] Re: Sharing no digit business

franktaw at netscape.net franktaw at netscape.net
Fri Apr 3 16:11:33 CEST 2009


Incidentally, this is an example of a sequence whose initial behavior 
is quite different from the limiting behavior.  It starts out looking 
like most numbers will appear in the sequence; but in fact it has 
density 0.  It can't include any number that has all nine non-zero 
digits, and those have density 1.

The description should say "positive integer", rather than just 
"integer".  It might also be interesting to look at the zero-based 
version of this sequence, starting with a(0) = 1.  I think this starts:

1,0,3,2,5,4,7,6,9,8,11,20,13,22,15,23,17,24,19,25,31

Franklin T. Adams-Watters


-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

Hello SeqFans,
I'm still in the "Sharing no digit" business... Could
someone please check this seq:

"a(n) shares no digit with the a(n)th term of the sequence"

a(1)=2 -- and to extend the seq, always add the smallest
          integer not used so far.

S = 2,1,4,3,6,5,8,7,10,9,12,30,14,20,16,22,18,23,21,31,33,34,...

(a nightmare to do by hand)

Best,
E.

(terms *not* in S are also of interest: 11,13,15,17,19,...)







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