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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.

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