A242039 List of integers b such that (a1,b,c1) and (a2,b,c2) are primitive Eisenstein triples, max(a1,b,c1,a2,c2)=b, and a1,c1,a3,c3 are distinct.

280, 1144, 1155, 1680, 1768, 1976, 2145, 2584, 2805, 3003, 3128, 3315, 3360, 3400, 3496, 3705, 3800, 4095, 4600, 4845, 5005, 5280, 5336, 5355, 5704, 5720, 5800, 5865, 5985, 6160, 6200, 6240, 6545, 6555, 6783, 6864, 7192, 7280, 7315, 7400, 7735, 8120, 8265, 8584, 8645, 8680, 8835, 8855, 9176, 9177, 9240, 9360, 9512, 9976

Offset: 1

Author

Albert Lau, Aug 12 2014

Keywords

• nonn

Comments

For Eisenstein triple see A121992.

Examples

			280 is in the list because (93,280,247) and (19,280,271) are primitive Eisenstein triples and 280 is the largest side and no other side is equal.
Consider (3,8,7) and (5,8,7), 8 is not in the list because 7 appear in both triple.
		

Crossrefs

Cf. A089025, A121992.

Programs

Mathematica

max = 2000;
data = Do[Sqrt[-3 a^2 + 4 c^2] // If[IntegerQ[#] && GCD[a, c] == 1, {a, (a + #)/2, c} // Sow] &, {a, max}, {c, Sqrt[3]/2 a // Ceiling, a - 1}] // Reap // Last // Last;
Select[data[[;; , 1]] // Tally, #[[2]] > 1 &][[;; , 1]]