A198463 - OEIS

%I #11 Feb 17 2025 01:30:49

%S 3,7,12,18,6,11,25,15,33,42,10,15,52,30,63,36,75,14,19,27,88,102,75,

%T 117,18,23,42,65,133,150,30,39,168,22,27,60,92,187,102,207,42,54,228,

%U 22,26,31,81,250,51,135,273,147,297,30,35,105,322,45,66,84,348

%N 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 See A198453.

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134.

%H Ron Knott, <a href="https://r-knott.surrey.ac.uk/pythag/pythag.html">Pythagorean Triples and Online Calculators</a>.

%e 2*5 + 3*6 = 4*7

%e 3*6 + 7*10 = 8*11

%e 4*7 + 12*15 = 13*16

%e 5*8 + 18*21 = 19*22

%e 6*9 + 6*9 = 9*12

%e 6*9 + 11*14 = 13*16

%o (True BASIC)

%o input k

%o for a = (abs(k)-k+4)/2 to  40

%o for b = a to (a^2+abs(k)*a+2)/2

%o   let t = a*(a+k)+b*(b+k)

%o    let c =int((-k+ (k^2+4*t)^.5)/2)

%o     if c*(c+k)=t then print a; b; c,

%o next b

%o print

%o next a

%o end

%Y Cf. A103606, A198453-A198462, A198464-A198469.

%K nonn

%O 1,1

%A _Charlie Marion_, Nov 26 2011