Prime Hyperfibonacci numbers

[Jonathan Post]

Thank you Peter, Joshua, and Maximilian,

I shall credit you when I submit the resulting sequences.

To answer Peter's question, I do not have Mathematica.  The seqs where
I gave Mathematica code were done on a library PC at Caltech, which
does have a license.

My first draft of the hyperfibonacci primes was done by typing in odd
values not ending in 5, into n the prime-testing Alpertron, as on a
Linux machine I'm using which does not properly support javascript, or
something like that, so that I could nether paste into nor copy from
the browser application.  I consider that "semiautomated" as opposed
to "by hand" where I use pen and paper, or nothing more than a
4-banger calculator.

It seems to me that seqfans are flexible and/or diverse in sometimes
submitting seqs done "by hand" and inviting more work with a "more",
while others have essentially supercomputer resources.

There's a related seq that I submitted 3 Apr 08 which gives a table of
hyperlucas numbers, from the same  Ayhan Dil and Istvan Mezo arXiv
reference linked to from A136431.  We shall likewise have a chance to
find the primes in that array. At which point the analysis of T. D.
Noe might be a good guide.

Noe, T. D. and Post, J. V. "Primes in Fibonacci n-step and Lucas
n-Step Sequences." J. Integer Seq. 8, Article 05.4.4, 2005.
http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Noe/noe5.html

And then Dil and Mezo give formulae including generating functions for
hyperharmonic numbers.

Now, back to ruthless editorial cutting of a 21-page paper as
presented at an international conference by myself and a co-author to
the 8-pages that the Proceedings editor is rigidly enforcing, and for
which I'm woefully overdue.

Best,

Jonathan Vos Post