cp's OEIS Frontend

A198466 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = -1, ordered by a and then b; sequence gives a values.

%I A198466 #8 Jul 07 2016 23:48:50
%S A198466 3,4,5,6,6,7,7,8,9,9,10,10,10,11,11,12,12,12,13,13,13,14,14,15,15,15,
%T A198466 15,15,16,16,16,17,18,18,18,18,19,19,19,19,20,20,20,21,21,21,21,21,22,
%U A198466 22,22,22,22,23,23,24,24,24,25,25,25,25,26,26,26,26,27,27,27,27,28,28,28,28,28
%N A198466 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = -1, ordered by a and then b; sequence gives a values.
%C A198466 The definition can be generalized to define Pythagorean k-triples a<=b<c where (a^2+b^2-c^2)/(c-a-b)=k, or where for some integer k, a(a+k) + b(b+k) = c(c+k).  See A198453 for more about Pythagorean k-triples.
%D A198466 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198466 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Pythag/pythag.html">Pythagorean Triples and Online Calculators</a>
%e A198466 3*2 + 3*2 = 4*3
%e A198466 4*3 + 6*5 = 7*6
%e A198466 5*4 + 10*9 = 11*10
%e A198466 6*5 + 7*6 = 9*8
%e A198466 6*5 + 15*14 = 16*15
%o A198466 (True BASIC)
%o A198466 input k
%o A198466 for a = (abs(k)-k+4)/2 to  40
%o A198466 for b = a to (a^2+abs(k)*a+2)/2
%o A198466   let t = a*(a+k)+b*(b+k)
%o A198466    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198466     if c*(c+k)=t then print a; b; c,
%o A198466 next b
%o A198466 print
%o A198466 next a
%o A198466 end
%Y A198466 Cf. A103606, A198453-A198469.
%K A198466 nonn
%O A198466 1,1
%A A198466 _Charlie Marion_, Dec 19 2011