A215657 -id:A215657 - cp's OEIS frontend

A215656 Solution R of (2u)^2 = R^2 - pS^2, where p is the n-th prime of the form 4k+1.

147, 20522387091091, 89544370675021535714607142, 8801866915656397716021519532258687362772409962179980790374047406788427

Offset: 1

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Jonathan Sondow, Aug 19 2012

nonn

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.

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

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

Cf. A002144, A048954, A215615, A215657.

a(n) = sqrt(4*u^2 + p*S^2) with S = A215657(n), p = A002144(n), u = A215615(p).

cp's OEIS Frontend

A215656 Solution R 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

A215656 Solution R of (2*u)^2 = R^2 - p*S^2, where p is the n-th prime of the form 4k+1.

Views

Author

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Comments

Examples

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Crossrefs

Formula

A215656 Solution R of (2u)^2 = R^2 - pS^2, where p is the n-th prime of the form 4k+1.