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A198463 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives b values.

%I A198463 #11 Feb 17 2025 01:30:49
%S A198463 3,7,12,18,6,11,25,15,33,42,10,15,52,30,63,36,75,14,19,27,88,102,75,
%T A198463 117,18,23,42,65,133,150,30,39,168,22,27,60,92,187,102,207,42,54,228,
%U A198463 22,26,31,81,250,51,135,273,147,297,30,35,105,322,45,66,84,348
%N A198463 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives b values.
%C A198463 See A198453.
%D A198463 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198463 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A198463 2*5 + 3*6 = 4*7
%e A198463 3*6 + 7*10 = 8*11
%e A198463 4*7 + 12*15 = 13*16
%e A198463 5*8 + 18*21 = 19*22
%e A198463 6*9 + 6*9 = 9*12
%e A198463 6*9 + 11*14 = 13*16
%o A198463 (True BASIC)
%o A198463 input k
%o A198463 for a = (abs(k)-k+4)/2 to  40
%o A198463 for b = a to (a^2+abs(k)*a+2)/2
%o A198463   let t = a*(a+k)+b*(b+k)
%o A198463    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198463     if c*(c+k)=t then print a; b; c,
%o A198463 next b
%o A198463 print
%o A198463 next a
%o A198463 end
%Y A198463 Cf. A103606, A198453-A198462, A198464-A198469.
%K A198463 nonn
%O A198463 1,1
%A A198463 _Charlie Marion_, Nov 26 2011