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

1,1

Comments

For Eisenstein triple see A121992.

Links

Table of n, a(n) for n=1..54.

Example

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.

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]]

Crossrefs

Cf. A089025, A121992.

Sequence in context: A245208 A256708 A207075 * A234911 A234905 A187178

Adjacent sequences: A242036 A242037 A242038 * A242040 A242041 A242042

Keyword

nonn

Author

Albert Lau, Aug 12 2014

Status

approved