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

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

Table of n, a(n) for n=1..4.

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

Cf. A002144, A048954, A215615, A215656.

Sequence in context: A368189 A238842 A059755 * A157631 A085503 A271711

Adjacent sequences: A215654 A215655 A215656 * A215658 A215659 A215660

Keyword

nonn

Author

Jonathan Sondow, Aug 20 2012

Status

approved