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 A198453 Consider triples a<=b
 2, 2, 3, 3, 5, 6, 4, 9, 10, 5, 6, 8, 5, 14, 15, 6, 9, 11, 6, 20, 21, 7, 27, 28, 8, 10, 13, 8, 35, 36, 9, 13, 16, 9, 21, 23, 9, 44, 45, 10, 26, 28, 10, 54, 55, 11, 14, 18, 11, 20, 23, 11, 65, 66, 12, 17, 21, 12, 24, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The definition can be generalized to define Pythagorean k-triples a<=b0 and acute when k<0. When k=0, the triangles are Pythagorean, as in the Beiler reference and Ron Knott’s link. For all k, the area of a Pythagorean k-triangle ABC with a<=b to be primitive if and only if there are no integers r>1, s>0 such that = for some Pythagorean s-triple . Thus, every Pythagorean 1-triple is primitive. For every k>1, the set of Pythagorean k-triples contains some non-primitive triples. In particular, for d a proper divisor of k, it includes (k/d)*(a,b,c), where (a,b,c) is a Pythagorean d-triple. - Franklin T. Adams-Watters, Dec 01 2011 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, New York, 1964, pp. 104-134. LINKS Table of n, a(n) for n=1..60. Ron Knott, Pythagorean Triples and Online Calculators EXAMPLE 2*3 + 2*3 = 3*4 3*4 + 5*6 = 6*7 4*5 + 9*10 = 10*11 5*6 + 6*7 = 8*9 5*6 + 14*15 = 15*16 6*7 + 9*10 = 11*12 PROG (True BASIC) input k for a = (abs(k)-k+4)/2 to 40 for b = a to (a^2+abs(k)*a+2)/2 let t = a*(a+k)+b*(b+k) let c =int((-k+ (k^2+4*t)^.5)/2) if c*(c+k)=t then print a; b; c, next b print next a end CROSSREFS Cf. A103606, A198454-A198469. Sequence in context: A277321 A262365 A063988 * A345162 A316313 A325876 Adjacent sequences: A198450 A198451 A198452 * A198454 A198455 A198456 KEYWORD nonn AUTHOR Charlie Marion, Oct 25 2011 STATUS approved

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Last modified June 1 11:12 EDT 2023. Contains 363068 sequences. (Running on oeis4.)