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Regarding the above comment of T. D. Noe on the for form [3, 0, 5}. The ]: the class number h(-60) = 2 = A000003(15), and [1, 0, 15] is the principal reduced form, representing the primes given in A033212.
The form [3, 0, 5] represents the proper equivalence class of the second genus of forms of discriminant Disc = -60. The Legendre symbol for the odd primes, not 3 or 5, satisfy L(-3|p) = -1 and L(5/|p) = -1, leading to primes p == {17, 23, 47, 53} (mod 60). See the Buell reference, p. 52, for the two characters L(p|3) and L(p|5). The prime 2 is a solution to represented by the imprimitive reduced form [2, 2, 8] of Disc = -60. (End)
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Except for a(1) = 2 this sequence gives also Regarding the primes represented by domment of _T. D. Noe_ on the primitive reduced for form [3, 0, 5] of discriminant Disc = -60 = -4*3*5} above. The class number is h(-60) = 2 = A000003(15), and [1, 0, 15] is the principal reduced form, representing the primes given in A033212.
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From Wolfdieter Lang, Jun 08 2021: (Start)
Except for a(1) = 2 this sequence gives also the primes represented by the primitive reduced form [3, 0, 5] of discriminant Disc = -60 = -4*3*5. The class number is h(-60) = 2 = A000003(15), and [1, 0, 15] is the principal reduced form, representing the primes given in A033212.
The form [3, 0, 5] represents the proper equivalence class of the second genus of forms of discriminant Disc = -60. The Legendre symbol for the odd primes, not 3 or 5, satisfy L(-3|p) = -1 and L(5/p) = -1, leading to primes p == {17, 23, 47, 53} (mod 60). See the Buell reference, p. 52, for the two characters L(p|3) and L(p|5). The prime 2 is a solution to the imprimitive reduced form [2, 2, 8] of Disc =-60. (End)
D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 51-52.
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