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A215656
Solution R of (2*u)^2 = R^2 - p*S^2, where p is the n-th prime of the form 4k+1.
1
147, 20522387091091, 89544370675021535714607142, 8801866915656397716021519532258687362772409962179980790374047406788427
OFFSET
1,1
COMMENTS
p = A002144(n), u = A215615(p), and S = A215657(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(4*u^2 + p*S^2) with S = A215657(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) = 147.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Aug 19 2012
STATUS
approved