cp's OEIS Frontend

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.

%I A242039 #17 Sep 07 2014 08:48:09
%S A242039 280,1144,1155,1680,1768,1976,2145,2584,2805,3003,3128,3315,3360,3400,
%T A242039 3496,3705,3800,4095,4600,4845,5005,5280,5336,5355,5704,5720,5800,
%U A242039 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
%N 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.
%C A242039 For Eisenstein triple see A121992.
%e A242039 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.
%e A242039 Consider (3,8,7) and (5,8,7), 8 is not in the list because 7 appear in both triple.
%t A242039 max = 2000;
%t A242039 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;
%t A242039 Select[data[[;; , 1]] // Tally, #[[2]] > 1 &][[;; , 1]]
%Y A242039 Cf. A089025, A121992.
%K A242039 nonn
%O A242039 1,1
%A A242039 _Albert Lau_, Aug 12 2014