A215656 -id:A215656 - cp's OEIS frontend

A215657 Solution S of (2u)^2 = R^2 - pS^2, where p is the n-th prime of the form 4k+1.

65, 5691884464123, 2171769991015128035203320, 1634465653492219202324217583600006782459921190308836446038375668451525

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Jonathan Sondow, Aug 20 2012

nonn

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.

			2*A215615(5) = 2*11 = 22 and 22^2  = 147^2 - 5*65^2, so a(1) = 65.

Ezra Brown and Marc Chamberland, Generalizing Gauss's gem, Amer. Math. Monthly, 119 (Aug. 2012), 597-601.

Cf. A002144, A048954, A215615, A215656.

a(n) = sqrt((R^2 - 4*u^2)/p) with R = A215656(n), p = A002144(n), u = A215615(p).

cp's OEIS Frontend

A215657 Solution S of (2u)^2 = R^2 - pS^2, where p is the n-th prime of the form 4k+1.

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cp's OEIS Frontend

A215657 Solution S of (2*u)^2 = R^2 - p*S^2, where p is the n-th prime of the form 4k+1.

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Examples

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Formula

A215657 Solution S of (2u)^2 = R^2 - pS^2, where p is the n-th prime of the form 4k+1.