A196262 Positive integers a in primitive (1/4)-Pythagorean triples (a,b,c) satisfying a<=b, in order of increasing a and then increasing b.

2, 4, 5, 6, 7, 7, 9, 10, 11, 12, 13, 15, 15, 17, 19, 20, 20, 22, 22, 23, 23, 25, 25, 26, 28, 29, 31, 31, 32, 32, 32, 33, 34, 36, 37, 38, 38, 39, 39, 41, 41, 43, 44, 44, 46, 47, 47, 50, 52, 52, 52, 53, 54, 55, 55, 55, 55, 57, 58, 58, 59, 60, 61, 62, 63, 64, 64, 64, 64, 65, 65, 65, 67, 68, 68, 68

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.

Examples

			Primitive (1/4)-Pythagorean triples a,b,c where c^2=a^2+b^2+(1/4)*a*b:
  2,  2,  3
  4, 15, 16
  5, 32, 33
  6, 70, 71
  7, 20, 22
  7,192,193
  9, 44, 46
 10, 26, 29
 11, 20, 24
 12, 17, 22
		

Links

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

Crossrefs

Cf. A195770, A196259, A196263, A196264.

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(a$nops(F(a)),a=1..100);# Robert Israel, Dec 20 2024

Mathematica

(See A196259.)

Extensions

Corrected by Robert Israel, Dec 20 2024