A366398 - OEIS

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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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,7

LINKS

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

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

Adjacent sequences: A366395 A366396 A366397 * A366399 A366400 A366401

KEYWORD

nonn

AUTHOR

Felix Huber, Oct 09 2023

STATUS

approved