[seqfan] Trying to compute A002052 (Prime determinants of forms with class number 2)

[Sean A. Irvine]

In my quest to improve some of the early OEIS sequences, I have been
trying to reproduce A002052 (Prime determinants of forms with class
number 2). Suryanarayana's paper (which is only 2 pages) describes a
test for membership as:

"Let d = 3 (mod 4), d > 0. Let p denote any prime factor of d - x^2 (x
< sqrt(d)), p < sqrt(d). Then h(d) = 2 [i.e. d is in this sequence] if
p occurs as a "partial quotient" in the simple continued fraction for
sqrt(d)."

It is not clear to me, if the test must hold for all prime factors of
d - x^2 or just one of them.  But either way, I have been unable to
reproduce the sequence.  It is likely that I'm misunderstanding
something about the test.  Perhaps someone else could have a crack at
it?

Suryanarayana's paper is available here:

http://www.ias.ac.in/j_archive/proca/2/2/178-179/viewpage.html

Some of my data: In the following, the first column corresponds to d,
"primes" is a list of possible p satisfying condition above, and
"cfrac" is the continued fraction for sqrt(d), all these d should be
in the sequence except for d=83:

7 primes [2] cfrac [2, 1, 1, 1, 4]
11 primes [2] cfrac [3, 3, 6]
19 primes [2, 3] cfrac [4, 2, 1, 3, 1, 2, 8]
23 primes [2] cfrac [4, 1, 3, 1, 8]
31 primes [2, 3, 5] cfrac [5, 1, 1, 3, 5, 3, 1, 1, 10]
43 primes [2, 3] cfrac [6, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12]
47 primes [2] cfrac [6, 1, 5, 1, 12]
59 primes [2, 5] cfrac [7, 1, 2, 7, 2, 1, 14]
67 primes [2, 3, 7] cfrac [8, 5, 2, 1, 1, 7, 1, 1, 2, 5, 16]
71 primes [2, 5, 7] cfrac [8, 2, 2, 1, 7, 1, 2, 2, 16]
79 primes [2, 3, 5, 7] cfrac [8, 1, 7, 1, 16]
83 primes [2] cfrac [9, 9, 18]
103 primes [2, 3] cfrac [10, 6, 1, 2, 1, 1, 9, 1, 1, 2, 1, 6, 20]
107 primes [2, 7] cfrac [10, 2, 1, 9, 1, 2, 20]
127 primes [2, 3, 7] cfrac [11, 3, 1, 2, 2, 7, 11, 7, 2, 2, 1, 3, 22]
131 primes [2, 5] cfrac [11, 2, 4, 11, 4, 2, 22]
139 primes [2, 3, 5] cfrac [11, 1, 3, 1, 3, 7, 1, 1, 2, 11, 2, 1, 1,
7, 3, 1, 3, 1, 22]
151 primes [2, 3, 5, 7] cfrac [12, 3, 2, 7, 1, 3, 4, 1, 1, 1, 11, 1,
1, 1, 4, 3, 1, 7, 2, 3, 24]

Regards,
Sean.