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%I #7 Jan 19 2020 20:40:30
%S 1,1,1,2,1,2,1,2,2,1,1,2,2,3,1,3,3,1,2,2,1,3,1,2,3,2,1,3,2,1,3,4,2,4,
%T 1,3,2,3,1,3,4,2,4,1,2,4,1,3,3,2,3,1,2,4,1,4,4,5,2,3,4,2,1,3,3,1,2,5,
%U 4,2,1,3,4,5,1,4,2,3,3,2,4,1,5,5,3,4,1,5
%N Triangles with integer sides i <= j <= k sorted by area, and, in case of ties, lexicographically by side lengths (smallest first). The sequence gives shortest side i. The other sides are in A331252 and A331253.
%e List of first triangles:
%e n
%e | 16*A^2
%e | | i .... (this sequence)
%e | | | j .. (A331252)
%e | | | | k (A331253)
%e | | | | |
%e 1 3 1 1 1
%e 2 15 1 2 2
%e 3 35 1 3 3
%e 4 48 2 2 2
%e 5 63 1 4 4
%e 6 63 2 2 3
%e 7 99 1 5 5
%e 8 128 2 3 3
%e 9 135 2 3 4
%e 10 143 1 6 6
%e 11 195 1 7 7
%Y Cf. A316841, A316843, A316844, A316845, A316853, A317182, A331011.
%Y Cf. A331252 (middle side j), A331253 (longest side k).
%K nonn
%O 1,4
%A _Hugo Pfoertner_, Jan 19 2020