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A198459 Consider triples a<=b where (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives b values.

%I A198459 #13 Feb 17 2025 01:30:31
%S A198459 6,4,16,10,8,30,18,14,48,12,28,70,18,40,16,30,96,25,54,22,40,126,20,
%T A198459 33,70,160,26,42,88,24,64,198,52,108,30,78,240,28,40,63,130,54,286,34,
%U A198459 48,75,154,32,64,110,336,88,180,38,128,390,28,36,66,102,208,448,33,42
%N A198459 Consider triples a<=b<c where (a^2+b^2-c^2)/(c-a-b) = 2, ordered by a and then b; sequence gives b values.
%C A198459 See A198453 and A198457.
%D A198459 A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.
%H A198459 Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.
%e A198459 3*5 + 6*8 = 7*9
%e A198459 4*6 + 4*6 = 6*8
%e A198459 5*7 + 16*17 = 17*18
%e A198459 6*8 + 10*12 12*14
%e A198459 7*9 + 8*10 = 11*13
%e A198459 7*9 + 30*32 = 31*33
%o A198459 (True BASIC)
%o A198459 input k
%o A198459 for a = (abs(k)-k+4)/2 to  40
%o A198459 for b = a to (a^2+abs(k)*a+2)/2
%o A198459   let t = a*(a+k)+b*(b+k)
%o A198459    let c =int((-k+ (k^2+4*t)^.5)/2)
%o A198459     if c*(c+k)=t then print a; b; c,
%o A198459 next b
%o A198459 print
%o A198459 next a
%o A198459 end
%Y A198459 Cf. A103606, A198453-A198458, A198460-A198469.
%K A198459 nonn
%O A198459 1,1
%A A198459 _Charlie Marion_, Nov 15 2011