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 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 J. Bourgain, A. Gamburd, and P. Sarnak, Markoff triples and strong approximation, arXiv:1505.06411 [math.NT], 2015. 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 Intersection of A002808 and A002559. Complement of (A178444 union {1}) in A002559. Sequence in context: A321533 A212407 A190607 * A182585 A191593 A259944 Adjacent sequences:  A256392 A256393 A256394 * A256396 A256397 A256398 KEYWORD nonn,more AUTHOR Jonathan Sondow, Apr 30 2015 STATUS approved

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Last modified May 28 15:55 EDT 2020. Contains 334684 sequences. (Running on oeis4.)