A378675 Areas of trapezoids with exactly one pair of parallel sides having prime sides and height.

15, 21, 27, 27, 45, 45, 55, 63, 65, 81, 85, 85, 95, 99, 115, 117, 125, 125, 135, 145, 155, 171, 175, 175, 185, 189, 205, 207, 225, 235, 243, 245, 265, 275, 279, 295, 297, 315, 315, 325, 333, 335, 355, 365, 385, 387, 405, 407, 425, 451, 455, 459, 473, 475, 475

Offset

1,1

Links

Felix Huber, Table of n, a(n) for n = 1..2633

Felix Huber, Trapezoids having prime sides and height with area A

Example

27 is twice in the sequence because there are two distinct trapezoids [p, d, q, f, h] (p and q are parallel, height h) with prime sides and height and area 27: [13, 5, 5, 5, 3], [11, 3, 7, 5, 3].

Maple

with(NumberTheory):
A378675:=proc(A)
   local m, p, q, i, j, d, f, h, x, y, M, T;
   if isprime(A)=false and A>1 then
      T:=[];
      M:=map(x->A/x, select(isprime, (Divisors(A)) minus {2}));
      for m in M do
         for i to pi(floor(m-1/2)) do
            q:=ithprime(i);
            p:=2*m-q;
            if isprime(p) then
               h:=A/m;
         for x from max(4, floor((p-q+1)/2)) by 2 to (h^2-1)/2 do
            y:=p-q-x;
            if issqr(x^2+h^2) and issqr(y^2+h^2) then
               d:=isqrt(y^2+h^2);
               f:=isqrt(x^2+h^2);
               if isprime(d) and isprime(f) then
                  T:=[op(T), A]
               fi
            fi
         od
      fi
         od
      od;
      return op(T)
   fi;
end proc;
seq(A378675(A), A=1..475);

Crossrefs

Cf. A000040, A027750, A070088, A214602, A365049, A366398, A374594, A378148, A378149, A378150.

Sequence in context: A211375 A326387 A217078 * A138594 A131651 A134642

Adjacent sequences: A378672 A378673 A378674 * A378676 A378677 A378678

Keyword

nonn

Author

Felix Huber, Dec 04 2024

Status

approved