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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.
1
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.
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
Sequence in context: A245208 A256708 A207075 * A234911 A234905 A187178
KEYWORD
nonn
AUTHOR
Albert Lau, Aug 12 2014
STATUS
approved