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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
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
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Aug 20 2012
STATUS
approved