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A198462 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 3, ordered by a and then b; sequence gives a values.

%I A198462 #11 Feb 17 2025 01:30:44
%S A198462 2,3,4,5,6,6,6,7,7,8,9,9,9,10,10,11,11,12,12,12,13,14,14,15,15,15,15,
%T A198462 15,16,17,17,17,18,18,18,18,18,19,19,20,20,20,21,21,21,21,21,22,22,22,
%U A198462 23,23,24,24,24,24,25,25,25,25,26,26,27,27,27,27,27,28
%N A198462 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 values.
%C A198462 See A198453.
%D A198462 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198462 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A198462 2*5 + 3*6 = 4*7
%e A198462 3*6 + 7*10 = 8*11
%e A198462 4*7 + 12*15 = 13*16
%e A198462 5*8 + 18*21 = 19*22
%e A198462 6*9 + 6*9 = 9*12
%e A198462 6*9 + 11*14 = 13*16
%o A198462 (True BASIC)
%o A198462 input k
%o A198462 for a = (abs(k)-k+4)/2 to  40
%o A198462 for b = a to (a^2+abs(k)*a+2)/2
%o A198462   let t = a*(a+k)+b*(b+k)
%o A198462    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198462     if c*(c+k)=t then print a; b; c,
%o A198462 next b
%o A198462 print
%o A198462 next a
%o A198462 end
%Y A198462 Cf. A103606, A198453-A198461, A198463-A198469.
%K A198462 nonn
%O A198462 1,1
%A A198462 _Charlie Marion_, Nov 26 2011