A366398 a(n) is the number of distinct triangles with prime sides and whose perimeter is equal to the n-th prime.

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, 12, 15, 12, 20, 19, 16, 21, 21, 21, 25, 19, 17, 15, 20, 20, 25, 36, 41, 38, 39, 34, 26, 25, 30, 34, 31, 27, 34, 45, 36, 33, 42, 39, 33, 45, 47, 54, 55, 48, 50, 58

Offset: 1

Author

Felix Huber, Oct 09 2023

Keywords

• nonn

Examples

			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.
		

Links

• Felix Huber, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A070088.

Programs

Maple

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);