A075880 Position of the circles around (0,0) that contain record numbers of lattice points in the list of all circles around (0,0) that pass through lattice points, ordered by increasing radius.

0, 1, 4, 13, 30, 121, 362, 1232, 1584, 7121, 17548, 32649, 37603, 174926, 437750, 821432, 1198677, 5678338, 14335447, 27044791, 43735981, 209473053, 531787054, 1006745669, 2097411347, 8474384496, 10122355701

Offset: 1

Author

Hugo Pfoertner, Oct 16 2002

Keywords

• nonn

Comments

The first terms of this sequence were given by James Buddenhagen in a sci.math posting on May 05 2002 entitled "Circle with 3 lattice points"

Examples

			a(4)=13 because A001481(14) = A071383(4)=25.
		

Links

• James Buddenhagen, Circle with 3 lattice points, thread in NG sci.math.
• Hugo Pfoertner, Asymptotic Behavior of A075880(n)

Crossrefs

Cf. A001481, A064533, A071383, A230656.

Formula

a(n) = k-1 for which A001481(k) = A071383(n).

lim n ->infinity a(n) = k_LR * exp(n) / n^(1/2), where k_LR is the Landau-Ramanujan constant 0.764223653... (A064533)

Extensions

Minor edits to adjust formula and example for changes to offset of related sequences by Ray Chandler, Jan 13 2012