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As GH mentioned discriminant $p = 4 u^2 + 1,$ here is one with class number one:

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jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ 
jagy@phobeusjunior:~/old drive/home/jagy/Cplusplus$ ./indefCycle
Input three coefficients a b c for indef f(x,y)= a x^2 + b x y + c y^2 
1 1  -169

0  form   1 25 -13   delta  -1
1  form   -13 1 13   delta  1
2  form   13 25 -1   delta  -25
3  form   -1 25 13   delta  1
4  form   13 1 -13   delta  -1
5  form   -13 25 1   delta  25
6  form   1 25 -13
minimum was   1rep 1 0 disc   677 dSqrt 26.019223663  M_Ratio  677
Automorph, written on right of Gram matrix:  
-53  -1352
-104  -2653
 Trace:  -2706   gcd(a21, a22 - a11, a12) : 104
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Here we are using a theorem of Lagrange, that given an indefinite form with positive nonsquare discriminant $\Delta,$ then any nonzero integer $n$ primitively represented by the form, also satisfying $ |n| < \frac{1}{2} \sqrt \Delta,$ occurs as the first coefficient of at least one form in the cycle of adjacent equivalent reduced forms. This is Theorem 85 on page 111 of Introduction to the Theory of Numbers by Leonard Eugene Dickson (1929)

INSERTED::: I found the quote I really wanted, Buell top of page 79:

Aside from the exceptional discriminants of very small magnitude, an odd class number can only occur for an odd prime discriminant.

Here we are using a theorem of Lagrange, that given an indefinite form with positive nonsquare discriminant $\Delta,$ then any nonzero integer $n$ primitively represented by the form, also satisfying $ |n| < \frac{1}{2} \sqrt \Delta,$ occurs as the first coefficient of at least one form in the cycle of adjacent equivalent reduced forms. This is Theorem 85 on page 111 of Introduction to the Theory of Numbers by Leonard Eugene Dickson (1929). I do not see that Buell proves (or even quotes) the full Lagrange result, but his Theorem 3.18 on page 42 does the result for target $-4$ that we use here. An unusual, and quite pretty, description of the numbers represented by an indefinite binary is in pages 18-23 of The Sensual Quadratic Form by John Horton Conway. The presentation includes a method that quickly finds all represented numbers up to some bound in absolute value, this is the Climbing Lemma on page 11.

Here we are using a theorem of Legendre, that given an indefinite form with positive nonsquare discriminant $\Delta,$ then any integer $n$ primitively represented by the form, also satisfying $ |n| < \sqrt \Delta,$ occurs as the first coefficient of at least one form in the cycle of adjacent equivalent reduced forms.

Here we are using a theorem of Lagrange, that given an indefinite form with positive nonsquare discriminant $\Delta,$ then any nonzero integer $n$ primitively represented by the form, also satisfying $ |n| < \frac{1}{2} \sqrt \Delta,$ occurs as the first coefficient of at least one form in the cycle of adjacent equivalent reduced forms. This is Theorem 85 on page 111 of Introduction to the Theory of Numbers by Leonard Eugene Dickson (1929)