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A198461 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives a, b and c values in that order.

%I A198461 #11 Feb 17 2025 01:30:40
%S A198461 2,3,4,3,7,8,4,12,13,5,18,19,6,6,9,6,11,13,6,25,26,7,15,17,7,33,34,8,
%T A198461 42,43,9,10,14,9,15,18,9,52,53,10,30,32,10,63,64,11,36,38,11,75,76,12,
%U A198461 14,19,12,19,23,12,27,30,12,88,89,13,102,103,14,57,59,14,117,118
%N A198461 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives a, b and c values in that order.
%C A198461 See A198453.
%D A198461 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198461 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A198461 2*5 + 3*6 = 4*7
%e A198461 3*6 + 7*10 = 8*11
%e A198461 4*7 + 12*15 = 13*16
%e A198461 5*8 + 18*21 = 19*22
%e A198461 6*9 + 6*9 = 9*12
%e A198461 6*9 + 11*14 = 13*16
%o A198461 (True BASIC)
%o A198461 input k
%o A198461 for a = (abs(k)-k+4)/2 to  40
%o A198461 for b = a to (a^2+abs(k)*a+2)/2
%o A198461   let t = a*(a+k)+b*(b+k)
%o A198461    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198461     if c*(c+k)=t then print a; b; c,
%o A198461 next b
%o A198461 print
%o A198461 next a
%o A198461 end
%Y A198461 Cf. A103606, A198453-A198460, A198462-A198469.
%K A198461 nonn,tabf
%O A198461 1,1
%A A198461 _Charlie Marion_, Nov 26 2011