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A306676 Number of distinct acute triangles with prime sides and largest side = prime(n).

%I A306676 #12 May 03 2019 19:24:00
%S A306676 1,2,3,5,5,8,9,11,13,12,18,17,21,27,30,28,30,38,38,43,56,53,59,59,56,
%T A306676 64,79,85,100,106,79,90,96,115,102,123,124,130,144,147,152,177,161,
%U A306676 188,199,225,193,175,195,228,248,247,280,259,267,277,288,324
%N A306676 Number of distinct acute triangles with prime sides and largest side = prime(n).
%e A306676 For n=3, prime(n)=5. Acute triangles: {2,5,5}, {3,5,5}, {5,5,5} (Total=3=a(3)).
%e A306676 For n=4, prime(n)=7. Acute triangles: {2,7,7}, {3,7,7}, {5,5,7}, {5, 7, 7}, {7, 7, 7} (Total=5=a(4)).
%p A306676 #nType=1 for acute triangles, nType=2 for obtuse triangles
%p A306676 #nType=0 for both triangles
%p A306676 CountPrimeTriangles := proc (n, nType := 1)
%p A306676   local aa, oo, j, k, sg, a, b, c, tt, lAcute;
%p A306676   aa := {}; oo := {};
%p A306676   a := ithprime(n);
%p A306676   for j from n by -1 to 1 do
%p A306676     b := ithprime(j);
%p A306676     for k from j by -1 to 1 do
%p A306676       c := ithprime(k);
%p A306676       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 A306676         lAcute := evalb(0 < b^2+c^2-a^2);
%p A306676         tt := sort([a, b, c]);
%p A306676         if lAcute then aa := {op(aa), tt} else oo := {op(oo), tt} end if
%p A306676       end if
%p A306676     end do
%p A306676   end do;
%p A306676   return sort(`if`(nType = 1, aa, `if`(nType = 2, oo, `union`(aa, oo))))
%p A306676 end proc:
%Y A306676 Cf. A306673, A306674, A306677, A306678.
%K A306676 nonn
%O A306676 1,2
%A A306676 _César Eliud Lozada_, Mar 04 2019