%I #17 Dec 26 2024 20:00:59
%S 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,
%T 29,31,31,32,32,32,33,34,36,37,38,38,39,39,41,41,43,44,44,46,47,47,50,
%U 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
%N Positive integers a in primitive (1/4)-Pythagorean triples (a,b,c) satisfying a<=b, in order of increasing a and then increasing b.
%C See A195770 for definitions of k-Pythagorean triple, primitive k-Pythagorean triple, and lists of related sequences.
%H Robert Israel, <a href="/A196262/b196262.txt">Table of n, a(n) for n = 1..10000</a>
%e Primitive (1/4)-Pythagorean triples a,b,c where c^2=a^2+b^2+(1/4)*a*b:
%e 2, 2, 3
%e 4, 15, 16
%e 5, 32, 33
%e 6, 70, 71
%e 7, 20, 22
%e 7,192,193
%e 9, 44, 46
%e 10, 26, 29
%e 11, 20, 24
%e 12, 17, 22
%p F:= proc(a)
%p 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))
%p end proc:
%p seq(a$nops(F(a)),a=1..100);# _Robert Israel_, Dec 20 2024
%t (See A196259.)
%Y Cf. A195770, A196259, A196263, A196264.
%K nonn
%O 1,1
%A _Clark Kimberling_, Sep 30 2011
%E Corrected by _Robert Israel_, Dec 20 2024