Yet Another Coprimality-Based Number-triangle

Leroy Quet qq-quet at
Thu Sep 2 20:10:52 CEST 2004

[posted also to sci.math]

I submitted the following sequence to the OEIS earlier today:

%S A000001 1,2,3,5,7,4,6,8,9,11,13,17,19,10,12,14,15,16,21,23,25
%N A000001 Number-triangle where a(0,0) is 1, a(m,n) = lowest 
as-yet-unused (reading rows from left to right) positive integer
which is coprime to both a(m-1,n) and a(m-1,n-1)
(or is coprime to a(m-1,0) if n=0, or to a(m-1,m-1) if n=m).
%e A000001 a(3,2)=9 is lowest as-yet-unused positive integer coprime to 
both a(2,1)=7 and a(2,2)=4.
a(4,0)=13 is lowest as-yet-unused positive integer coprime to a(3,0)=6.
%O A000001 0
%K A000001 ,more,nonn,tabl,

Here are the integers above arranged into a triangle:

2, 3
5, 7, 4
6, 8, 9, 11

Is there a direct way to determine which row of the triangle any 
particular integer is in?

Leroy Quet

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