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%I #11 Apr 08 2014 06:07:53
%S 3,9,13,19,20,33,51,65,73,99,119,129,163,170,174,193,201,203,220,243,
%T 260,269,287,289,339,362,377,393,450,451,513,532,559,579,615,649,696,
%U 702,714,723,740,771,801,883,909,940,969,975,1059,1112,1153,1155,1156,1164,1251,1299,1325,1332,1353,1424,1455,1459,1569,1605,1615,1683,1690,1716,1801,1869,1919,1923
%N Consider primitive Heronian triangles with integer area and with sides {m, m+1, c}, where c > m+1. The sequence gives the possible values of m.
%C Corresponding values of c are 5, 17, 15, 37, 29, 65, 101, 109, 145.
%C And corresponding values of area/6 are 1, 6, 14, 19, 35, 44, 85, 330, 146, 231, 1190.
%C The sequence includes all terms of A016064 (where c = m+2) except for the first term, 1 (case with zero area).
%C Note that in all cases c is odd and m+2 <= c < 2m+1.
%e First triangle has sides (3,4,5) and area 6.
%e 2nd triangle has sides (9,10,17) and area 36.
%e 3rd triangle has sides (13,14,15) and area 84.
%t re=Reap[Do[a=m;b=m+1;Do[s=(a+b+c)/2;area=Sqrt[s(s-a)(s-b)(s-c)];If[IntegerQ[area],Sow[{a,b,c,area}];Break[]],{c,2m-1,m+2,-2 }],{m,3,2000}]][[2,1]];#[[1]]&/@ re
%Y Cf. A083875, A016064, A224301, A227003, A239978, A227166.
%K nonn
%O 1,1
%A _Zak Seidov_, Apr 03 2014
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