A215657 - OEIS

A215657

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

65, 5691884464123, 2171769991015128035203320, 1634465653492219202324217583600006782459921190308836446038375668451525

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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

STATUS

approved