[seqfan] A002335

israel at math.ubc.ca israel at math.ubc.ca
Fri Feb 15 09:26:22 CET 2013

It seems to me that the title and comment of A002335 do a poor job of 
explaining what is going on in this sequence. I could only figure it out by 
decyphering the Maple program. If p is the (n-1)'th prime for which a 
representation p = x^2 - 2 y^2 in positive integers exists, then A002335(n) 
is the least y for such a representation. Note that the representation is 
generally not unique, e.g. 17 = 5^2 - 2*2^2 = 7^2 - 2*4^2.

I also don't know why the offset is 2 here, unless it has something to do
with the fact that the first such prime is 2.

Robert Israel
University of British Columbia

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