A366398 - OEIS

%I #27 Oct 12 2023 01:51:57

%S 0,0,0,1,1,1,2,1,1,3,2,3,5,4,5,4,5,3,5,4,3,6,7,10,11,10,8,12,8,11,11,

%T 12,15,12,20,19,16,21,21,21,25,19,17,15,20,20,25,36,41,38,39,34,26,25,

%U 30,34,31,27,34,45,36,33,42,39,33,45,47,54,55,48,50,58

%N a(n) is the number of distinct triangles with prime sides and whose perimeter is equal to the n-th prime.

%H Felix Huber, <a href="/A366398/b366398.txt">Table of n, a(n) for n = 1..1000</a>

%e For n = 13 the a(13) = 5 distinct triangles with prime sides (u, v, w) are (3, 19, 19), (5, 17, 19), (7, 17, 17), (11, 11, 19), and (11, 13, 17). They all have perimeter 41, which is the 13th prime.

%p A366398 := proc(n) local u, v, w, a; u := 1; a := 0; while 2*ithprime(u) < ithprime(n) do v := u; while 2*ithprime(v) <= ithprime(n) - ithprime(u) do if ithprime(n) < 2*ithprime(u) + 2*ithprime(v) and isprime(ithprime(n) - ithprime(u) - ithprime(v)) then a := a + 1; end if; v := v + 1; end do; u := u + 1; end do; return a; end proc; seq(A366398(n), n = 1 .. 100);

%Y Cf. A070088.

%K nonn

%O 1,7

%A _Felix Huber_, Oct 09 2023