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<DIV>This is similar to the EKG sequence (A064413), except that A064413(n ), for
n >2, is always the lowest unpicked positive integer that is
not coprime with A064413(n-1). </DIV>
<DIV>Starting with the first term, it goes: 1, 2, 4, 6, 3, 9, 12, 8, 10,
5, 15 . . . (See <A
href="http://www.research.att.com/projects/OEIS?Anum=A064413">http://www.research.att.com/projects/OEIS?Anum=A064413</A>.)</DIV>
<DIV> </DIV>
<DIV>The EKG sequence is a permutation of the integers; it would be interesting
to see if this is too.</DIV>
<DIV> </DIV>
<DIV>My thanks go both to Leroy and Pieter Moree for their work on
my question about A018804.</DIV>
<DIV> </DIV>
<DIV>Best,</DIV>
<DIV>Matthew Vandermast</DIV>
<DIV> </DIV>
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<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV style="FONT: 10pt arial"><B>From:</B> <A
href="mailto:qq-quet@mindspring.com">Leroy Quet</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A
href="mailto:Seqfan@ext.jussieu.fr">Seqfan@ext.jussieu.fr</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, December 04, 2003 4:19
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> GCD>1 based sequence</DIV>
<DIV><BR></DIV>Unexpectedly, this sequence is not now in the EIS:<BR><BR>2, 4,
6, 3, 8, 9, 10, 5, 12, 14, 7, 15, 16, 18, 20,...<BR><BR><BR>a(1) = 2;<BR>a(m)
= lowest unpicked positive integer which is *not* coprime with at <BR>least
one previous term of the sequence.<BR><BR>By "unpicked", I mean the integer is
not among {a(1),...,a(m-1)}.<BR>And by "not coprime with at least one previous
term", I mean that at <BR>least one prime dividing a(m) also divides at least
one element of <BR>{a(1),...,a(m-1)}.<BR>(By these definitions are obvious, I
trust.)<BR><BR><BR>I could have sworn this sequence was at one time in the
EIS. Am I <BR>thinking of something similarly defined, or was the sequence
eliminated <BR>because each term was, say, 1/2 of another sequence's term? (I
have not <BR>put this into Superseeker.)<BR><BR> <BR>It seems like this
(new?) sequence might be a permutation of the integers <BR>>= 2.<BR><BR>(It
might be advantageous to define a(0) = 1 for whatever reason. {I am <BR>sure
there is a good reason for doing such, but I am unsure now
why}.)<BR><BR>thanks,<BR>Leroy Quet<BR><BR></BLOCKQUOTE></DIV></BODY></HTML>