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 A215657 Solution S of (2*u)^2 = R^2 - p*S^2, where p is the n-th prime of the form 4k+1. 1
 65, 5691884464123, 2171769991015128035203320, 1634465653492219202324217583600006782459921190308836446038375668451525 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS p = A002144(n), u = A215615(p), and R = A215656(n). A215615 is computed from Wendt's circulant determinant A048954. Brown and Chamberland (2012, p. 600) give explicit formulas for u, R, S. LINKS Ezra Brown and Marc Chamberland, Generalizing Gauss's gem, Amer. Math. Monthly, 119 (Aug. 2012), 597-601. FORMULA a(n) = sqrt((R^2 - 4*u^2)/p) with R = A215656(n), p = A002144(n), u = A215615(p). EXAMPLE 2*A215615(5) = 2*11 = 22 and 22^2  = 147^2 - 5*65^2, so a(1) = 65. CROSSREFS Cf. A002144, A048954, A215615, A215656. Sequence in context: A035519 A238842 A059755 * A157631 A085503 A271711 Adjacent sequences:  A215654 A215655 A215656 * A215658 A215659 A215660 KEYWORD nonn AUTHOR Jonathan Sondow, Aug 20 2012 STATUS approved

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)