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A198464 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives c values.

%I A198464 #11 Feb 17 2025 01:31:36
%S A198464 4,8,13,19,9,13,26,17,34,43,14,18,53,32,64,38,76,19,23,30,89,103,59,
%T A198464 118,24,28,42,67,134,151,35,43,169,29,33,63,94,188,104,208,47,58,229,
%U A198464 31,34,38,84,251,56,137,274,149,298,39,43,108,323,52,71,88,349
%N A198464 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives c values.
%C A198464 See A198453.
%D A198464 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198464 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A198464 2*5 + 3*6 = 4*7
%e A198464 3*6 + 7*10 = 8*11
%e A198464 4*7 + 12*15 = 13*16
%e A198464 5*8 + 18*21 = 19*22
%e A198464 6*9 + 6*9 = 9*12
%e A198464 6*9 + 11*14 = 13*16
%o A198464 (True BASIC)
%o A198464 input k
%o A198464 for a = (abs(k)-k+4)/2 to  40
%o A198464 for b = a to (a^2+abs(k)*a+2)/2
%o A198464   let t = a*(a+k)+b*(b+k)
%o A198464    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198464     if c*(c+k)=t then print a; b; c,
%o A198464 next b
%o A198464 print
%o A198464 next a
%o A198464 end
%Y A198464 Cf. A103606, A198453-A198463, A198465-A198469.
%K A198464 nonn
%O A198464 1,1
%A A198464 _Charlie Marion_, Nov 26 2011