A196263 Positive integers b in primitive (1/4)-Pythagorean triples (a,b,c) satisfying a<=b, in order of increasing a and then increasing b.

2, 15, 32, 70, 20, 192, 44, 26, 20, 17, 220, 32, 884, 160, 64, 39, 391, 102, 950, 228, 2080, 32, 348, 186, 253, 1100, 416, 3780, 55, 77, 247, 608, 754, 1271, 1792, 310, 2838, 64, 5984, 96, 940, 340, 265, 629, 190, 960, 8692, 1634, 115, 287, 2655, 3680, 5734, 84, 468, 1316, 11904, 1820, 90, 938

Offset: 1

Author

Clark Kimberling, Sep 30 2011

Keywords

• nonn

Comments

See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A195770, A196259, A196262, A196264, A196260.

Programs

Maple

F:= proc(a)
  sort(select(t -> subs(t, b) >= a and subs(t, c) > 0 and igcd(a, subs(t,b),subs(t,c)) = 1, [isolve](4*a^2 + 4*b^2 + a*b = 4*c^2)), (s, t) -> subs(s, b) <= subs(t, b))
end proc:
seq(op(map(t -> subs(t, b), F(a))), a=1..100); # Robert Israel, Dec 20 2024

Mathematica

(See A196259.)

Extensions

Corrected by Robert Israel, Dec 25 2024