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A198458 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives a values.

%I A198458 #15 Feb 16 2025 21:24:40
%S A198458 3,4,5,6,7,7,8,9,9,10,10,11,12,12,13,13,13,14,14,15,15,15,16,16,16,17,
%T A198458 18,18,18,19,19,19,20,20,21,21,21,22,22,22,22,23,23,24,24,24,24,25,25,
%U A198458 25,25,26,26,27,27,27,28,28,28,28,28,29,30,30,30,30,30,30,31,31,31
%N A198458 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives a values.
%C A198458 See A198453 and A198457.
%D A198458 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198458 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A198458 3*5 + 6*8 = 7*9
%e A198458 4*6 + 4*6 = 6*8
%e A198458 5*7 + 16*17 = 17*18
%e A198458 6*8 + 10*12 12*14
%e A198458 7*9 + 8*10 = 11*13
%e A198458 7*9 + 30*32 = 31*33
%o A198458 (True BASIC)
%o A198458 input k
%o A198458 for a = (abs(k)-k+4)/2 to  40
%o A198458 for b = a to (a^2+abs(k)*a+2)/2
%o A198458   let t = a*(a+k)+b*(b+k)
%o A198458    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198458     if c*(c+k)=t then print a; b; c,
%o A198458 next b
%o A198458 print
%o A198458 next a
%o A198458 end
%Y A198458 Cf. A103606, A198453-A198457, A198459-A198469.
%K A198458 nonn
%O A198458 1,1
%A A198458 _Charlie Marion_, Nov 15 2011