%I #8 Feb 18 2017 13:02:21

%S 65,5691884464123,2171769991015128035203320,

%T 1634465653492219202324217583600006782459921190308836446038375668451525

%N Solution S of (2*u)^2 = R^2 - p*S^2, where p is the n-th prime of the form 4k+1.

%C p = A002144(n), u = A215615(p), and R = A215656(n).

%C A215615 is computed from Wendt's circulant determinant A048954.

%C Brown and Chamberland (2012, p. 600) give explicit formulas for u, R, S.

%H Ezra Brown and Marc Chamberland, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.119.07.597">Generalizing Gauss's gem</a>, Amer. Math. Monthly, 119 (Aug. 2012), 597-601.

%F a(n) = sqrt((R^2 - 4*u^2)/p) with R = A215656(n), p = A002144(n), u = A215615(p).

%e 2*A215615(5) = 2*11 = 22 and 22^2 = 147^2 - 5*65^2, so a(1) = 65.

%Y Cf. A002144, A048954, A215615, A215656.

%K nonn

%O 1,1

%A _Jonathan Sondow_, Aug 20 2012