OFFSET
1,1
COMMENTS
Conjecture: lim_{n->oo} a(n)/n = Pi. Also, lim_{n->oo} A354571(n)/n = Pi.
REFERENCES
Lothar Selle, Kleines Handbuch Pythagoreische Zahlentripel, Books on Demand, 4th impression 2022, chapter 2.2.1; see chapter 2.3.10 for identity of lim_(n->oo) A354571(n)/n.
EXAMPLE
3 is a term: 3^2 + 4^2 = 5^2, so the triangle with sides (3,4,5) is a Pythagorean triangle; GCD(3,4,5) = 1, so it is primitive; and the odd leg length, 3, has no prime factors p that are not congruent to 3 (mod 4).
5 is not a term: it is the odd leg length of the primitive Pythagorean triangle (5,12,13), but 5 (a prime) == 1 (mod 4).
21 (whose prime factors are 3 and 7, both of which are congruent to 3 (mod 4)) is listed twice because it is the odd leg length of two primitive Pythagorean triangles ((20,21,29) and (21,220,221)).
CROSSREFS
KEYWORD
nonn
AUTHOR
Lothar Selle, Jun 03 2022
STATUS
approved