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A198460 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives c values.

%I A198460 #13 Feb 17 2025 01:30:35
%S A198460 7,6,17,12,11,31,20,17,49,16,30,71,22,42,21,33,97,29,56,27,43,127,26,
%T A198460 37,72,161,32,46,90,31,67,199,56,110,37,81,241,36,46,67,132,59,287,42,
%U A198460 54,79,156,41,69,113,337,92,182,47,131,391,40,46,72,106,210,449,45,52
%N A198460 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives c values.
%C A198460 See A198453 and A198457.
%D A198460 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198460 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A198460 3*5 + 6*8 = 7*9
%e A198460 4*6 + 4*6 = 6*8
%e A198460 5*7 + 16*17 = 17*18
%e A198460 6*8 + 10*12 12*14
%e A198460 7*9 + 8*10 = 11*13
%e A198460 7*9 + 30*32 = 31*33
%o A198460 (True BASIC)
%o A198460 input k
%o A198460 for a = (abs(k)-k+4)/2 to  40
%o A198460 for b = a to (a^2+abs(k)*a+2)/2
%o A198460   let t = a*(a+k)+b*(b+k)
%o A198460    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198460     if c*(c+k)=t then print a; b; c,
%o A198460 next b
%o A198460 print
%o A198460 next a
%o A198460 end
%Y A198460 Cf. A103606, A198453-A198459, A198461-A198469.
%K A198460 nonn
%O A198460 1,1
%A A198460 _Charlie Marion_, Nov 15 2011