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A198454 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 A198454 #20 Feb 16 2025 10:25:56
%S A198454 2,3,4,5,5,6,6,7,8,8,9,9,9,10,10,11,11,11,12,12,12,13,13,14,14,14,14,
%T A198454 14,15,15,15,16,17,17,17,17,18,18,18,18,19,19,19,20,20,20,20,20,21,21,
%U A198454 21,21,21,22,22,23,23,23,24
%N A198454 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 A198454 See A198453.
%D A198454 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198454 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>
%e A198454 2*3 + 2*3 = 3*4
%e A198454 3*4 + 5*6 = 6*7
%e A198454 4*5 + 9*10 = 10*11
%e A198454 5*6 + 6*7 = 8*9
%e A198454 5*6 + 14*15 = 15*16
%e A198454 6*7 + 9*10 = 11*12
%o A198454 (True BASIC)
%o A198454 input k
%o A198454 for a = (abs(k)-k+4)/2 to  40
%o A198454 for b = a to (a^2+abs(k)*a+2)/2
%o A198454   let t = a*(a+k)+b*(b+k)
%o A198454    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198454     if c*(c+k)=t then print a;b;c,
%o A198454 next b
%o A198454 print
%o A198454 next a
%o A198454 end
%Y A198454 Cf. A009004, A198453-A198469.
%K A198454 nonn
%O A198454 1,1
%A A198454 _Charlie Marion_, Oct 26 2011