
EXAMPLE

a(1) = 4 because H[4, 2, 2] = sqrt((sqrt(2) + 1)*(sqrt(2)  1)) = 1.
a(40) = 100 because H[100, 89, 89] = sqrt(25*(5 + sqrt(89))*(5 + sqrt(89))) = sqrt(1600) = 40.
In both cases there are also no lexicographically earlier Heron square root triple that take this value.
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The first few triples are:
[ 4, 2, 2] > 1; [40, 29, 25] > 13; [68, 58, 50] > 25;
[ 5, 5, 4] > 2; [35, 35, 28] > 14; [65, 65, 52] > 26;
[ 9, 8, 5] > 3; [36, 34, 34] > 15; [72, 65, 53] > 27;
[10, 10, 8] > 4; [40, 40, 32] > 16; [65, 65, 64] > 28;
[17, 13, 8] > 5; [41, 40, 37] > 17; [73, 68, 61] > 29;
[15, 15, 12] > 6; [45, 45, 36] > 18; [72, 68, 68] > 30;
[20, 17, 13] > 7; [52, 50, 34] > 19; [85, 68, 65] > 31;
[20, 20, 16] > 8; [50, 50, 40] > 20; [80, 80, 64] > 32;
[26, 20, 18] > 9; [52, 49, 45] > 21; [85, 73, 72] > 33;
[25, 25, 20] > 10; [55, 55, 44] > 22; [82, 80, 74] > 34;
[34, 26, 20] > 11; [58, 52, 50] > 23; [98, 82, 68] > 35;
[30, 30, 24] > 12; [60, 60, 48] > 24; [89, 81, 80] > 36;
