%I #12 Apr 14 2019 10:50:06
%S 1,3,16,1,5,8,24,640,1,7,40,195,32,3,534000,1,9,106000,3,12754704,40,
%T 8,6525,226592,1,11,2968,15,1039424,16,48,305,352,3621,1856,1,13,9384,
%U 126585,1360,8,896073208080,56,72664,3,6440,5,521904,1,15,140510608,5
%N Minimal (positive) solution a(n) of Pell equation b(n)^2 - D(n)*a(n)^2 = +4 with D(n)= A077425(n). The companion sequence is a(n)=A077428(n).
%C For the conversion of the (x,y) values of Perron's table to the (b(n),a(n)) values see a A077428 comment.
%C For the general solution of Pell b^2 - D(n)*a^2 = +4 see a comment in A077428 (with a and b interchanged).
%D O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, Satz 3.35, p. 109 and table p. 108).
%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Class number theory</a>
%H Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%t d = Select[Range[5, 300, 4], !IntegerQ[Sqrt[#]]&]; a[n_] := Module[{a, b, r}, b /. {r = Reduce[a > 0 && b > 0 && a^2 - d[[n]]*b^2 == 4, {a, b}, Integers]; (r /. C[1] -> 0) || (r /. C[1] -> 1) // ToRules} // Select[#, IntegerQ, 1] &] // First; Table[a[n], {n, 1, 52}] (* _Jean-François Alcover_, Jul 30 2013 *)
%K nonn
%O 1,2
%A _Wolfdieter Lang_, Nov 29 2002
%E More terms from _Max Alekseyev_, Mar 03 2010