Integer Triangle: nth row not coprime to (n-1)th row

From: Leroy Quet (qqquet_at_mindspring.com)
Date: 02/01/05 

Date: 1 Feb 2005 11:20:30 -0800

I submitted the following to the Encyclopedia of Integer Sequences:
http://www.research.att.com/~njas/sequences/index.html#L

>%S A000001 1,2,3,4,6,8,9,10,12,14,5,7,15,16,18,20,21,22,24,25,26
>%N A000001 a(1) = 1, a(2) = 2, a(3) = 3;
>triangle where nth row has lowest n positive integers not yet in the
sequence
>such that each integer has a prime divisor in common with at least one

>element of the (n-1)th row.
>%C A000001 Is this a permutation of the positive integers?
>%e A000001 7 is in the 5th row because it does not occur earlier and
14 is
>in the 4th row.
>%O A000001 1
>%K A000001 ,more,nonn,tabl,

>%S A000001 2,4,6,3,8,9,10,12,14,15,5,7,16,18,20,21,22,24,25,26,27
>%N A000001 a(1) = 2;
>triangle where nth row has lowest n positive integers not yet in the
sequence
>such that each integer has a prime divisor in common with at least one

>element of the (n-1)th row.
>%C A000001 Is this a permutation of the integers >= 2?
>%e A000001 7 is in the 5th row because it does not occur earlier and
14 is
>in the 4th row.
>%O A000001 1
>%K A000001 ,more,nonn,tabl,

Are these sequences a permutation of the positive integers
and a permutation of the integers >=2?

These triangles remind me of sequence A064413 (the EKG sequence) and
sequence A089088.
(Showing sequence A064413 is a permutation of the positive integers is
more tricky than showing sequence A089088 is a permutation, or so I
have
been led to believe.)

thanks,
Leroy Quet

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