[seqfan] a result which I don't understand

[David Newman]

I tried an experiment with Mathematica and I can't find any rationale for
the result I got.  Perhaps there's someone out there who can understand
what's going  on.  Maybe there's room for a sequence here.

I ask Mathematica for an instance of  a[1] not equal to a[2] not equal to
a[3]...not equal to a[k] .  A human might respond with  1,2,3,...,k, but
not so Mathematica.  For example, for k=3, using the Code

FindInstance[a[1]!=a[2]!=a[3],{a[1],a[2],a[3]},Integers].  Mathematica
responds with 2,1,4.

I've copied and pasted the results of the first five computations, I hope
the arrows come through okay.

{{a[1]2,a[2]1}}

{{a[1]2,a[2]1,a[3]4}}

{{a[1]15,a[2]5,a[3]13,a[4]19}}

{{a[1]9,a[2]1,a[3]7,a[4]10,a[5]-3}}

{{a[1]-2,a[2]2,a[3]-4,a[4]3,a[5]-6,a[6]6}}

Does anyone understand what's going on here?