GCD>1 based sequence

[Matthew Vandermast]

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).  
Starting with the first term, it goes:  1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15 . . .  (See http://www.research.att.com/projects/OEIS?Anum=A064413.)

The EKG sequence is a permutation of the integers; it would be interesting to see if this is too.

My thanks go both to Leroy and Pieter Moree for their work on my question about A018804.

Best,
Matthew Vandermast

  ----- Original Message ----- 
  From: Leroy Quet 
  To: Seqfan at ext.jussieu.fr 
  Sent: Thursday, December 04, 2003 4:19 PM
  Subject: GCD>1 based sequence


  Unexpectedly, this sequence is not now in the EIS:

  2, 4, 6, 3, 8, 9, 10, 5, 12, 14, 7, 15, 16, 18, 20,...


  a(1) = 2;
  a(m) = lowest unpicked positive integer which is *not* coprime with at 
  least one previous term of the sequence.

  By "unpicked", I mean the integer is not among {a(1),...,a(m-1)}.
  And by "not coprime with at least one previous term", I mean that at 
  least one prime dividing a(m) also divides at least one element of 
  {a(1),...,a(m-1)}.
  (By these definitions are obvious, I trust.)


  I could have sworn this sequence was at one time in the EIS. Am I 
  thinking of something similarly defined, or was the sequence eliminated 
  because each term was, say, 1/2 of another sequence's term? (I have not 
  put this into Superseeker.)

   
  It seems like this (new?) sequence might be a permutation of the integers 
  >= 2.

  (It might be advantageous to define a(0) = 1 for whatever reason. {I am 
  sure there is a good reason for doing such, but I am unsure now why}.)

  thanks,
  Leroy Quet

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