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A306677 Number of distinct obtuse triangles with prime sides and largest side = prime(n).

%I A306677 #11 May 03 2019 19:24:15
%S A306677 0,1,1,1,2,3,4,7,8,10,11,13,16,19,23,28,30,33,37,44,45,52,59,65,67,75,
%T A306677 78,88,93,103,107,117,123,129,139,141,153,161,174,182,192,194,212,217,
%U A306677 234,240,254,265,279,283,297,316,317,343,356,368,380,382,404
%N A306677 Number of distinct obtuse triangles with prime sides and largest side = prime(n).
%e A306677 For n=5, prime(n)=11. Triangles: {5, 7, 11}, {7, 7, 11}, so a(5) = 2.
%e A306677 For n=6, prime(n)=13. Triangles: {3, 11, 13}, {5, 11, 13}, {7, 7, 13}, so a(6)=3.
%p A306677 #nType=1 for acute triangles, nType=2 for obtuse triangles
%p A306677 #nType=0 for both triangles
%p A306677 CountPrimeTriangles := proc (n, nType := 1)
%p A306677   local aa, oo, j, k, sg, a, b, c, tt, lAcute;
%p A306677   aa := {}; oo := {};
%p A306677   a := ithprime(n);
%p A306677   for j from n by -1 to 1 do
%p A306677     b := ithprime(j);
%p A306677     for k from j by -1 to 1 do
%p A306677       c := ithprime(k);
%p A306677       if a < b+c and abs(b-c) < a and b < c+a and abs(c-a) < b and c < a+b and abs(a-b) < c then
%p A306677         lAcute := evalb(0 < b^2+c^2-a^2);
%p A306677         tt := sort([a, b, c]);
%p A306677         if lAcute then aa := {op(aa), tt} else oo := {op(oo), tt} end if
%p A306677       end if
%p A306677     end do
%p A306677   end do;
%p A306677   return sort(`if`(nType = 1, aa, `if`(nType = 2, oo, `union`(aa, oo))))
%p A306677 end proc:
%Y A306677 Cf. A306673, A306674, A306676, A306678.
%K A306677 nonn
%O A306677 1,5
%A A306677 _César Eliud Lozada_, Mar 04 2019