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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 (list; graph; refs; listen; history; text; internal format)
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

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(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

Cf. A002144, A048954, A215615, A215657.

Sequence in context: A075925 A097729 A214139 * A308889 A214619 A061154

Adjacent sequences:  A215653 A215654 A215655 * A215657 A215658 A215659

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Aug 19 2012

STATUS

approved

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)