login
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.
3
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
1,3
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"
LINKS
James Buddenhagen, Circle with 3 lattice points, thread in NG sci.math.
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)
EXAMPLE
a(4)=13 because A001481(14) = A071383(4)=25.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Oct 16 2002
EXTENSIONS
Minor edits to adjust formula and example for changes to offset of related sequences by Ray Chandler, Jan 13 2012
STATUS
approved