A071383

[John Conway]

On Fri, 31 May 2002, cloitre quoted:

> %N A071383 Squared radius of first circle around (0,0) with more points of
> the square lattice on its circumference than on any smaller circle around
> (0,0).

   This description should be cleaned up - how about "Squared radii of
the circles around (0,0) that contain record numbers of lattice points." ?

cloitre also wrote

> >From listed terms I noticed : 1<A071383(n+1)/A071383(n)<=5

   This is obvious.  One can multiply the points  x+iy  for which  
x^2 + y^2 = N  either  2+i  or  2-i  to get two new sets of points  X+iY  
for which  X^2 + Y^2 = 5N.  This strictly increases the number since it's
easy to see that the two sets aren't the same.  So the answer to:

> Is there any value of n such that A071383(n+1)/A071383(n)>5 ?

is "No".

> About the asymptotic behaviour of A071383 :
> 
> Does lim n-->infinity Log(A071383(n))/n = 1 ?

   I think I can answer this one too, the answer probably being "yes".

   John Conway