A215656 - OEIS

%I #12 Nov 05 2025 15:35:34

%S 147,20522387091091,89544370675021535714607142,

%T 8801866915656397716021519532258687362772409962179980790374047406788427

%N Solution R 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 S = A215657(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="https://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(4*u^2 + p*S^2) with S = A215657(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) = 147.

%Y Cf. A002144, A048954, A215615, A215657.

%K nonn

%O 1,1

%A _Jonathan Sondow_, Aug 19 2012