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A366398
a(n) is the number of distinct triangles with prime sides and whose perimeter is equal to the n-th prime.
2
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
1,7
EXAMPLE
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.
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);
CROSSREFS
Cf. A070088.
Sequence in context: A227310 A291905 A347584 * A365932 A240853 A363094
KEYWORD
nonn
AUTHOR
Felix Huber, Oct 09 2023
STATUS
approved