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

1,1

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

Example

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

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.)

Crossrefs

Cf. A195770, A196259, A196263, A196264.

Sequence in context: A287076 A344587 A100006 * A238461 A195994 A182815

Adjacent sequences: A196259 A196260 A196261 * A196263 A196264 A196265

Keyword

nonn

Author

Clark Kimberling, Sep 30 2011

Extensions

Corrected by Robert Israel, Dec 20 2024

Status

approved