|
|
A256395
|
|
Composite Markoff numbers.
|
|
3
|
|
|
34, 169, 194, 610, 985, 1325, 4181, 6466, 9077, 10946, 14701, 37666, 51641, 62210, 75025, 135137, 195025, 196418, 294685, 499393, 646018, 925765, 1136689, 1278818, 1346269, 1441889, 2012674, 2423525, 3524578
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Bourgain, Gamburd, and Sarnak have announced a proof that almost all Markoff numbers A002559 are composite. Equivalently, the prime Markoff numbers A178444 have density zero among all Markoff numbers. (It is conjectured that infinitely many Markoff numbers are prime.)
See A002559 for references, links, and additional comments.
|
|
LINKS
|
|
|
MATHEMATICA
|
Rest[Select[m = {1};
Do[x = m[[i]]; y = m[[j]]; a = (3*x*y + Sqrt[-4*x^2 - 4*y^2 + 9*x^2*y^2])/2;
b = (3*x*y + Sqrt[-4*x^2 - 4*y^2 + 9*x^2*y^2])/2;
If[IntegerQ[a], m = Union[Join[m, {a}]]];
If[IntegerQ[b], m = Union[Join[m, {b}]]], {n, 8}, {i, Length[m]}, {j, i}];
Take[m, 50], ! PrimeQ[#] &]]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|