

A215657


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


1




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), 597601.


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: A035519 A238842 A059755 * A157631 A085503 A271711
Adjacent sequences: A215654 A215655 A215656 * A215658 A215659 A215660


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Aug 20 2012


STATUS

approved



